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BY \.-VvO; 





/* *" 


IN COMPLIANCE with many requests, I beg to offer to 
the public a series of popular Lectures which I have 
delivered on various occasions. They are designed for 
readers who, without being professionally occupied with 
the study of Natural Science, are yet interested in the 
scientific results of such studies. The difficulty, felt so 
stro'ngly in printed scientific lectures, namely, that the 
reader canno f see the experiments, has in the present 
case been materially lessened by the numerous illustra- 
tions which the publishers have liberally furnished. 

The first and second Lectures have already appeared 
in print; the first in a university programme which, 
however, was not published. The second appeared in 
the 'Kieler Monatsschrift ' for May, 1853, but owing to 
the restricted circulation of that journal, became but 
little known ; both have, accordingly, been reprinted. 
The third and fourth Lectures have not previously 

These Lectures, called forth as they have been by 
incidental occasions, have not, of course, been composed 
in accordance with a rigidly uniform plan. Each of 
them has been kept perfectly independent of the others. 


Hence some amount of repetition has been unavoidable, 
and the first four may perhaps seem somewhat confusedly 
thrown together. If I may claim that they have any 
leading thought, it would be that I have endeavoured 
to illustrate the essence and the import of Natural 
laws, and their relation to the mental activity of man. 
This seems to me the chief interest and the chief need 
in Lectures before a public whose education has been 
mainly literary. 

I have but little to remark with reference to individual 
Lectures. The set of Lectures, which treats of the Theory 
of Vision, have been already published in the c Preussische 
Jahrbiicher,' and have acquired, therefore, more of the 
character of Review articles. As it was possible in 
this second reprint to render many points clearer by 
illustrations, I have introduced a number of woodcuts, 
and inserted in the text the necessary explanations. A 
few other small alterations have originated in my having 
availed myself of the results of new series of experiments. 

The fifth Lecture, on the Interaction of Natural Forces, 
originally published sixteen years ago, could not be left 
entirely unaltered in this reprint. Yet the alterations 
have been as slight as possible, and have merely been 
such as have become necessary by new experimental 
facts, which partly confirm the statements originally 
made, and partly modify them. 

The seventh Lecture, on the Conservation of Force, 
developes still further a portion of the fifth. Its main 
object is to elucidate the cardinal physical ideas of work, 
and of its unalterability. The applications and con- 
sequences of the law of the Conservation of Force are 
comparatively more easy to grasp. They have in recent 


times been treated by several persons in a vivid and 
interesting manner, so that it seemed unnecessary to 
publish the corresponding part of the cycle of lectures 
which I delivered on this subject ; the more so as some of 
the more important subjects to be discussed will, perhaps 
in the immediate future, be capable of more definite 
treatment tnan is at present possible. 

On the other hand, I have invariably found that the 
fundamental ideas of this subject always appear difficult 
of comprehension not only to those who have not passed 
through the school of mathematical mechanics ; but even 
to those who attack the subject with diligence and in- 
telligence, and who possess a tolerable acquaintance \vith 
natural science. It is not to be denied that these ideas 
are abstractions of a quite peculiar kind. Even such a 
mind as that of Kant found difficulty in comprehend- 
ing them ; as is shown by his controversy with Leibnitz. 
Hence I thought it worth while to furnish in a popular form 
an explanation of these ideas, by referring them to many 
of the better known mechanical and physical examples ; 
and therefore I have only for the present given the first 
Lecture of that series which is devoted to this object. 

The last Lecture was the opening address for the 
' Naturforscher-Versammlung,' in Innsbruck. It was 
not delivered from a complete manuscript, but from 
brief notes, and was not written out until a year after. 
The present form has, therefore, no claim to be con- 
sidered an accurate reproduction of that address. I have 
added it to the present collection, for in it I have treated 
briefly what is more fully discussed in the other articles. 
Its title to the place which it occupies lies in the fact 
that it attempts to bring the views enunciated in the 


preceding Lectures into a more complete and more com- 
prehensive whole. 

In conclusion, I hope that these Lectures may meet 
with that forbearance which lectures always require when 
they are not heard, but are read in print. 



IN bringing this Translation of Helmholtz's Popular 
Scientific Lectures before the public, I have to thank 
Mr. A. J. Ellis for having placed at the disposal of the 
Publishers the translation of the third Lecture ; and also 
Dr. Francis, the Editor of the c Philosophical Magazine,' 
for giving me permission to use the translation of the 
fifth Lecture, which originally appeared in that Journal. 
In addition to the Editorial charge of the book, my 
own task has been limited to the translation of two of 
the Lectures. I should have hesitated to undertake the 
work, had I not from the outset been able to rely upon 
the aid of several gentlemen whose names are appended 
to the Contents. One advantage gained from this division 
of labour is, that the publication of the work has been 
accelerated ; but a far more important benefit has been 
secured to it, in the co-operation of translators who have 
brought to the execution of their task special knowledge 
of their respective subjects. 


March 1873. 



GENERAL. Translated by H. W. EVE, Esq., M^A., F.C.S., 
Wellington College 1 


EVE, Esq. 33 


Translated by A. J. ELLIS, Esq., M.A., F.R.S. ... 61 

IV. ICE AND GLACIERS. Translated by -Dr. ATKINSON, F.C.S., 

Professor of Experimental Science, Staff College . . .107 


by Professor TYNDALL, LL.D., F.R.S 153 


by Dr. PYE-SMITH, B.A., F.R.C.P., Guys Hospital : 

I. The Eye as an Optical Instrument . . . .197 

IT. The Sensation of Sight . . . . . .229 

m. The Perception of Sight 270 


KINSON .317 


by Dr. W. FLIGHT, F.C.S., British Museum . . . .363 


IN the year 1850, when I was a student in the Univer- 
sity of Marburg, it was my privilege to translate for 
the ' Philosophical Magazine ' the celebrated memoirs of 
Clausius, then just published, on the Moving Force of 

In 1851, through the liberal courtesy of the late Pro- 
fessor Magnus, I was enabled to pursue my scientific 
labours in his laboratory in Berlin. One evening during 
my residence there my friend Dr. Du Bois-Eaymond put I 
a pamphlet into my hands, remarking that it was ' the I 
production of the first head in Europe since the death of 
Jacobi,' and that it ought to be translated into English. 
Soon after my return to England I translated the essay and 
published it in the ' Scientific Memoirs,' then brought out 
under the joint-editorship of Huxley, Henfrey, Francis, 
and myself. 

This essay, which was communicated in 1847 to the 
Physical Society of Berlin, has become sufficiently famous 
since. It was entitled ' Die Erhaltung der Kraft,' and 
its author was Helmholtz, originally Military Physician 
in the Prussian service, afterwards Professor of Physiology 
in the Universities of Konigsberg and Heidelberg, and 
now Professor of Physics in the University of Berlin. 

Brought thus face to face with the great generalisation 
of the Conservation of Energy, I sought, to the best of 
my ability, to .master it by independent thought in all its 
physical details,- I could not forget rny indebtedness to 


Helmholtz and Clausius, or fail to see the probable in- 
fluence of their writings on the science of the coming 
time. For many years, therefore, it was my habit to 
place every physical paper published by these eminent 
men within the reach of purely English readers. 

The translation of the lecture on the ' Wechselwirkung 
der Naturkrafte,' printed in the following series, had this 
origin. It appears herewith the latest emendations of 
the author introduced by Dr. Atkinson. 

The evident aim of these Lectures is to give to those 
' whose education has been mainly literary,' an intelligent 
interest in the researches of science. Even among such 
persons the reputation of Helmholtz is so great as to 
render it almost superfluous for me to say that the intel- 
lectual nutriment here offered is of the very first quality. 

Soon after the publication of the ' Tonempfindungen ' 
bv Helmholtz, I endeavoured to interest the Messrs. Long- 
man in the work, urging that the publication of a trans- 
lation of it would be an honour to their house. The} 
went carefully into the question of expense, took sage 
counsel regarding the probable sale, and came reluctantly 
to the conclusion that it would not be remunerative. 1 
I then recommended the translation of these c Populare 
Vortrage,' and to this the eminent publishers immediately 

Hence the present volume, brought out under the 
editorship of Dr. Atkinson of the Staff College, Sandhurst. 
The names of the translators are, I think, a guarantee 
that their work will be worthy of their original. 


March 1873. 

1 Since the date of the foregoing letter fr..,m Professor Tyndall, Messrs. 
Longman & Co. have made arrangements for the translation of Helmholtz'g 
Tonempfindungen, by Mr. Alexander J. Ellis, F.R.S., &c. 



NOVEMBER 22, 1862, 


TO-DAY we are met, according to annual custom, in 
grateful commemoration of an enlightened sovereign of 
this kingdom, Charles Frederick, who, in an age when 
the ancient fabric of European society seemed tottering 
to its fall, strove, with lofty purpose and untiring zeal, to 
promote the welfare of his subjects, and, above all, their 
moral and intellectual development. Eightly did he 
judge that by no means could he more effectually realise 
this beneficent intention than by the revival and the 
encouragement of this University. Speaking, as I do, on 
such an occasion, at once in the name and in the pre- 

1 The German word Nalurwissenschaft has no exact equivalent ill 
modern English, including, as it does, both the Physical and the Natural 
Sciences. Curiously enough, in the original charter of the Royal Society, 
the phrase Natural Knowledge covers the same ground, but is there used in 
opposition to supernatural knowledge. (Note in Buckle's Civilisation, 
vol. ii. p. 341.) TB. 


sence of the whole University, I have thought it well to 
try and take, as far as is permitted by the narrow stand- 
point of a single student, a general view of the connection 
of the several sciences, and of their study. 

It may, indeed, "be thought that, at the present day, 
those relations between the different sciences which have 
led us to combine them under the name Universitas Lit- 
terarum, have become looser than ever. We see scholars 
and scientific men absorbed in specialities of such vast 
extent, that the most universal genius cannot hope to 
master more than a small section of our present range of 
knowledge. For instance, the philologists of the last 
three centuries found ample occupation in the study of 
Greek and Latin ; at best they added to it the know- 
ledge of two or three European languages, acquired for 
practical purposes. But now comparative philology aims 
at nothing less than an acquaintance with all the lan- 
guages of all branches of the human family, in order 
to deduce from them the laws by which language itself 
has been formed, and to this gigantic task it has already 
applied itself with superhuman industry. Even classical 
philology is no longer restricted to the study of those 
works which, by their artistic perfection and precision of 
thought, or because of the importance of their contents, 
have become models of prose and poetry to all ages. On 
the contrary, we have learnt that every lost fragment of 
an ancient author, every gloss of a pedantic grammarian, 
every allusion of a Byzantine court-poet, every broken 
tombstone found in the wilds of Hungary or Spain or 
Africa, may contribute a fresh fact, or fresh evidence, and 
thus serve to increase our knowledge of the past. And 
so another group of scholars are busy with the vast 
scheme of collecting and cataloguing, for the use of their 
successors, every available relic of classical antiquity, 


Add to this, in history, the study of original documents, 
the critical examination of parchments and papers accumu- 
lated in the archives of states and of towns ; the combi- 
nation of details scattered up and down in memoirs, in 
correspondence, and in biographies ; the deciphering of 
hieroglyphics and cuneiform inscriptions ; in natural 
history the more and more comprehensive classification 
of minerals, plants, and animals, as well living as extinct ; 
and there opens out before us an expanse of knowledge 
the contemplation of which may well bewilder us. In all 
these sciences the range of investigation widens as fast as 
the means of observation improve. The zoologists of past 
times were content to have described the teeth, the hair, 
the feet, and other external characteristics of an animal. 
The anatomist, on the other hand, confined himself to 
human anatomy, so far as he could make it out by the 
help of the knife, the saw, and the scalpel, with the 
occasional aid of injections of the vessels. Human 
anatomy then passed for an unusually extensive and diffi- 
cult study. Now we are no longer satisfied with the 
comparatively rough science which bore the name of 
human anatomy, and which, though without reason, was 
thought to be almost exhausted. We have added to it 
comparative anatomy that is, the anatomy of all animals 
--and microscopic anatomy, both of them sciences of 
infinitely wider range, which now absorb the interest of 

The four elements of the ancients and of mediaeval 
alchemy have been increased to sixty-four, the last four 
of which are due to a method invented in our own 
University, which promises still further discoveries. 1 But 

1 That is (he method of spectrum analysis, due to Bunsen and Kirchoff> 
both of Heidelberg. The elements alluded to are caesium rubidium, 
thallium, and iridium. 


not merely is the number of the elements far greater, the 
methods of producing complicated combinations of them 
have been so vastly improved, that what is called organic 
chemistry, which embraces only compounds of carbon with 
oxygen, hydrogen, nitrogen, and a few other elements, has 
already taken rank as an independent science. 

' As the stars of heaven for multitude ' was in ancient 
times the natural expression for a number beyond our 
comprehension, Pliny even thinks it almost presumption 
(' rem etiam Deo improbam ') on the part of Hipparchus 
to have undertaken to count the stars and to determine 
their relative positions. And yet none of the catalogues 
up to the seventeenth century, constructed without the 
aid of telescopes, give more than from 1,000 to 1,500 
stars of magnitudes from the first to the fifth. At pre- 
sent several observatories are engaged in continuing these 
catalogues down to stars of the tenth magnitude. So 
that upwards of 200,000 fixed stars are to be catalogued 
and their places accurately determined. The immediate 
result of these observations has been the discovery of a 
great number of new planets ; so that, instead of the six 
known in 1781, there are now seventy-five. 1 

The contemplation of this astounding activity in all 
branches of science may well make us stand aghast at 
the audacity of man, and exclaim with the Chorus in the 
'Antigone': 'Who can survey the whole field of know- 
ledge ? Who can grasp the clues, and then thread the 
labyrinth?' One obvious consequence of this vast exten- 
sion of the limits of science is, that every student is 
forced to choose a narrower and narrower field for his own 
studies, and can only keep up an imperfect acquaintance 
even with allied fields of research. It almost raises a 
smile to hear that in the seventeenth century Kepler was 

1 At the end of November 1864, the 82nd of the small planets, Alcmene. 
was discovered. There are now 109. 


invited to Gratz as professor of mathematics and moral 
philosophy ; and that at Leyden, in the beginning of the 
eighteenth, Boerhave occupied at the same time the chairs 
of botany, chemistry, and clinical medicine, and therefore 
practically that of pharmacy as well. At present we 
require at least four professors, or, in an university with 
its full complement of teachers, seven or eight, to repre- 
sent all these branches of science. And the same is true 
of other faculties. 

One of my strongest motives for discussing to-day the 
connection of the different sciences is that I am myself a 
student of natural philosophy ; and that it has been made 
of late a reproach against natural philosophy that it has 
struck out a path of its own, and has separated itself more 
and more widely from the other sciences which are united 
by common philological and historical studies. This op- 
position has, in fact, been long apparent, and seems to me 
to have grown up mainly under the influence of the 
Hegelian philosophy, or, at any rate, to harve been brought 
out into more distinct relief by that philosophy. Cer- 
tainly, at the end of the last century, when the Kantian 
philosophy reigned supreme, such a schism had never 
been proclaimed ; on the contrary, Kant's philosophy 
rested on exactly the same ground as the physical 
sciences, as is evident from his own scientific works, es- 
pecially from his ' Cosmogony,' based upon Newton's Law 
of Gravitation, which afterwards, under the name of 
Laplace's Nebular Hypothesis, came to be universally 
recognised. The sole object of Kant's ' Critical Phi- 
losophy ' was to test the sources and the authority of our 
knowledge, and to fix a definite scope and standard for 
the researches of philosophy, as compared with other 
sciences. According to his teaching, a principle disco- 
vered a priori by pure thought was a rule applicable to 
the method of pure thought, and nothing further ; it 


could . contain no real, positive knowledge. The Phi- 
losophy of Identity ' l was bolder. It started with the 
hypothesis that not only spiritual phenomena, but even 
the actual world nature, that is, and man were the 
result of an act of thought on the part of a creative 
mind, similar, it was supposed, in kind to the human 
mind. On this hypothesis it seemed competent for the 
human mind, even without the guidance of external ex- 
perience, to think over again the thoughts of the Creator, 
and to rediscover them by its own inner activity. Such 
was the view with which the fc Philosophy of Idertity ' set 
to work to construct a priori the results of other sciences. 
The process might be more or less successful in matters of 
theology, law, politics, language, art, history, in short, in 
all sciences, the subject-matter of which really grows out 
of our moral nature, and which are therefore properly 
classed together under the name of moral sciences. The 
state, the church, art, and language,' exist in order to 
satisfy certain moral needs of man. Accordingly, what- 
ever obstacles nature, or chance, or the rivalry of other 
men may interpose, the efforts of the human mind to 
satisfy its needs, being systematically directed to one 
end, must eventually triumph over all such fortuitous 
hindrances. Under these circumstances, it would not be 
a downright impossibility for a philosopher, starting from 
an exact knowledge of the mind, to predict the general 
course of human development under the above-named 
conditions, especially if he has before his eyes a basis of 
observed facts, on which to build his abstractions. More- 
over, Hegel was materially assisted, in his attempt to 
solve this problem, by the profound and philosophical 
views on historical and scientific subjects, with which the 
writings of his immediate predecessors, both poets and 

1 So called because it proclaimed the identity not only of subject and 
object, but of contradictories, such as existence and non-existence. TR. 


philosophers, abound. He had, for the most part, only to 
collect and combine them, in order to produce a system 
calculated to impress people by a number of acute and 
original observations. He thus succeeded in gaining the 
enthusiastic approval of most of the educated men of his 
time, and in raising extravagantly sanguine hopes of 
solving the deepest enigma of human life ; all the more 
sanguine doubtless, as the connection of his system was 
disguised under a strangely abstract phraseology, and was 
perhaps really understood by but few of his worshippers. 

But even granting that Hegel was more or less suc- 
cessful in constructing, a priori, the leading results of 
the moral sciences, still it was no proof of the correctness 
of the hypothesis of Identity, with which he started. 
The facts of nature would have been the crucial test. 
That in the moral sciences traces of the activity of the 
human intellect and of the several stages of its develop- 
ment should present themselves, was a matter of course ; 
but surely, if nature really reflected the result of the 
thought of a creative mind, the system ought, without 
difficulty, to find a place for her comparatively simple 
phenomena and processes. It was at this point that 
Hegel's philosophy, we venture to say, utterly broke 
down. His system of nature seemed, at least to natural 
philosophers, absolutely crazy. Of all the distinguished 
scientific men who were his contemporaries, not one was 
found to stand up for his ideas. Accordingly, Hegel 
himself, convinced of the importance of winning for 
his philosophy in the field of physical science that recog- 
nition which had been so freely accorded to it elsewhere, 
launched out, with unusual vehemence and acrimony, 
against the natural philosophers, and especially against 
Sir Isaac Newton, as the first and greatest representative 
of physical investigation. The philosophers accused the 
scientific men of narrowness ; the scientific men retorted 


that the philosophers were crazy. And so it came about 
that men of science began to lay some stress on the 
banishment of all philosophic influences from their work ; 
while some of them, including men of the greatest acute- 
ness, went so far as to condemn philosophy altogether, 
not merely as useless, but as mischievous dreaming. 
Thus, it must be confessed, not only were the illegitimate 
pretensions of the Hegelian system to subordinate to 
itself all other studies rejected, but no regard was paid 
to the rightful claims of philosophy, that is, the criticism 
of the sources of cognition', and the definition of the 
functions of the intellect. 

In the moral sciences the course of things was dif- 
ferent, though it ultimately led to almost the same 
result. In all branches of those studies, in theology, 
politics, jurisprudence, aesthetics, philology, there started 
up enthusiastic Hegelians, who tried to reform their 
several departments in accordance with the doctrines of 
their master, and, by the royal road of speculation, to 
reach at once the promised land and gather in the 
harvest, which had hitherto only been approached by 
long and laborious study. And so, for some time, a hard 
and fast line was drawn between the moral and the 
physical sciences ; in fact, the very name of science was 
often denied to the latter. 

The feud did not long subsist in its original intensity. 
The physical sciences proved conspicuously, by a brilliant 
ssries of discoveries and practical applications, that they 
contained a healthy germ of extraordinary fertility ; it 
was impossible any longer to withhold from them recog- 
nition and respect. And even in other departments of 
science, conscientious investigators of facts soon pro- 
tested against the over-bold flights of speculation. Still, 
it cannot be overlooked that the philosophy of Hegel and 
Schelling did exercise a beneficial influence ; since their 


time the attention of investigators in the moral sciences 
had been constantly and more keenly directed to the 
scope of those sciences, and to their intellectual con- 
tents, and therefore the great amount of labour bestowed 
on those systems has not been entirely thrown away. 

We see, then, that in proportion as the experimental 
investigation of facts has recovered its importance in the 
moral sciences, the opposition between them and the 
physical sciences has become less and less marked. Yet 
we must not forget that, though this opposition was 
brought out in an unnecessarily exaggerated form by the 
Hegelian philosophy, it has its foundation in the nature 
of things, and must, sooner or later, make itself felt. It 
depends partly on the nature of the intellectual processes 
the two groups of sciences involve, partly, as their very 
names imply, on the subjects of which they treat. It is 
not easy for a scientific man to convey to a scholar or a 
jurist a clear idea of a complicated process of nature ; 
he must demand of them a certain power of abstraction 
from the phenomena, as well as a certain skill in the use 
of geometrical and mechanical conceptions, in which it is 
difficult for them to follow him. On the other hand an 
artist or a theologian will perhaps find the natural philo- 
sopher too much inclined to mechanical and materinl 
explanations, which seem to them commonplace, and 
chilling to their feeling and enthusiasm. Nor will the 
scholar or the historian, who have some common ground 
with the theologian and the jurist, fare better with the 
natural philosopher. They will find him shockingly 
indifferent to literary treasures, perhaps even more in- 
different than he ought to be to the history of his own 
science. In short, there is no denying that, while the 
moral sciences deal directly with the nearest and dearest 
interests of the human mind, and with the institutions 
it has brought into being, the natural sciences are con- 


cerned with dead, indifferent matter, obviously indispen- 
sable for the sake of its practical utility, but apparently 
without any immediate bearing on the cultivation of the 

It has been shown, then, that the sciences have 
branched out into countless ramifications, that there has 
grown up between different groups of them a real and 
deeply-felt opposition, that finally no single intellect can 
embrace the whole range, or even a considerable por- 
tion of it. Is it still reasonable to keep them together 
in one place of education? Is the union of the four 
Faculties to form one University a mere relic of the 
Middle Ages ? Many valid arguments have been adduced 
for separating them. Why not dismiss the medical 
faculty to the hospitals of our great towns, the scientific 
men to the Polytechnic Schools, and form special semin- 
aries for the theologians and jurists? Long may the 
German universities be preserved from such a fate ! 
Then, indeed, would the connection between the dif- 
ferent sciences be finally broken. How essential that 
connection is, not only from an university point of view, 
as tending to keep alive the intellectual energy of the 
country, but also on material grounds, to secure the 
successful application of that energy, will be evident 
from a few considerations. 

First, then, I would say that union of the different 
Faculties is necessary to maintain a healthy equilibrium 
among the intellectual energies of students. Each study 
tries certain of our intellectual faculties more than the 
rest, and strengthens them accordingly by constant exer- 
cise. But any sort of one-sided development is attended 
with danger ; it disqualifies us for using those faculties 
that are less exercised, and so renders us less capable of 
a general view ; above all it leads us to overvalue our- 
selves. Anyone who has found himself much more sue- 


cessful than others in some one department of intellectual 
labour, is apt to forget that there are many other things 
which they can do better than he can : a mistake I 
would have every student remember which is the worst 
enemy of all intellectual activity. 

How many men of ability have forgotten to practise 
that criticism of themselves which is so essential to the 
student, and so hard to exercise, or have been completely 
crippled in their progress, because they have thought 
dry, laborious drudgery beneath them, and have devoted 
all their energies to the quest of brilliant theories and 
wonder-working discoveries ! How many such men have 
become bitter misanthropes, and put an end to a melan- 
choly existence, because they have failed to obtain among 
their fellows that recognition which must be won by 
labour and results, but which is ever withheld from 
mere self-conscious genius I Ancjl the more isolated a 
man is, the more liable is he to this danger ; while, 
on the other hand, nothing is more inspiriting than to 
feel yourself forced to strain every nerve to win the 
admiration of men whom you, in your turn, must 

In comparing the intellectual processes involved in the 
pursuit of the several branches of science, we are struck by 
certain generic differences, dividing one group of sciences 
from another. At the same time it must not be forgotten 
that every man of conspicuous ability has his own special 
mental constitution, which fits him for one line of 
thought rather than another. Compare the work of 
two contemporary investigators even in closely-allied 
branches of science, and you will generally be able to 
convince yourself that the more distinguished the men 
are, the more clearly does their individuality come out, 
and the less qualified would either of them be to carry 
on the other's researches. To-day I can, of course, dc 


nothing more than characterise some of the most general 
of these differences. 

I have already noticed the enormous mass of the 
materials accumulated by science. It is obvious that 
the organisation and arrangement of them must be pro- 
portionately perfect, if we are not to be hopelessly lost in 
the maze of erudition. One of the reasons why we can 
so far surpass our predecessors in each individual study 
is that they have shown us how to organise our know- 

This organisation consists, in the first place, of a 
mechanical arrangement of materials, such as is to be 
found in our catalogues, lexicons, registers, indexes, 
digests, scientific and literary annuals, systems of natural 
history, and the like. By these appliances thus much 
at least is gained, that such knowledge as cannot be 
carried about in the memory is immediately accessible to 
anyone who wants it. With a good lexicon a school-boy 
of the present day can achieve results in the interpreta- 
tion of the classics, which an Erasmus, with the erudition 
of a lifetime, could hardly attain. Works of this kind 
form, so to speak, our intellectual principal, with the 
interest of which we trade ; it is, so to speak, like 
capital invested in land. The learning buried in cata- 
logues, lexicons, and indexes looks as bare and uninviting 
as the soil of a farm ; the uninitiated cannot see or ap- 
preciate the labour and capital already invested there ; 
to them the work of the ploughman seems infinitely 
dull, weary, and monotonous. But though the compiler 
of a lexicon or of a system of natural history must be 
prepared to encounter labour as weary and as obstinate 
as the ploughman's, yet it need not be supposed that his 
work is of a low type, or that it is by any means as dry 
and mechanical as it looks when we have it before us in 
black and white. In this, as in any other sort of scien- 


tific work, it is necessary to discover every fact by 
careful observation, then to verify and collate them, and 
to separate what is important from what is not. All 
this requires a man with a thorough grasp, both of the 
object of the compilation, and of the matter and methods 
of the science ; and for such a man every detail has its 
bearing on the whole, and its special interest. Otherwise 
dictionary-making would be the vilest drudgery imagin- 
able. 1 That the influence of the progressive development 
of scientific ideas extends to these works is obvious from 
the constant demand for new lexicons, new natural 
histories, new digests, new catalogues of stars, all denot- 
ing advancement in the art of methodising and organis- 
ing science. 

But our knowledge is not to lie dormant in the shape 
of catalogues. The very fact that we must carry it about 
in black and white shows that our intellectual mastery of 
it is incomplete. It is not enough to be acquainted with 
the facts; scientific knowledge begins only when their 
laws and their causes are unveiled. Our materials must 
be worked up by a logical process ; and the first step is to 
connect like with like, and to elaborate a general concep- 
tion embracing them all. Such a conception, as the 
name implies, takes a number of single facts together, 
and stands as their representative in our mind. We call 
it a general conception, or the conception of a genus, 
when it embraces a number of existing objects ; we call it 
a law when it embraces a series of incidents or occurrences. 
When, for example, I have made out that all mammals 
that is, all warm-blooded, viviparous^ animals breathe 
through lungs, have two chambers in the heart and at 
least three tympanal bones, I need no longer remember 
these anatomical peculiarities in the individual cases of 
the monkey, the dog, the horse, and the whale ; the 

1 Condendaque lexica mandat damnatis. TR. 


general rule includes a vast number of single instances, 
and represents them in my memory. When I enunciate 
the law of refraction, not only does this law embrace all 
cases of rays falling at all possible angles on a plane sur- 
face of water, and inform me of the result, but it includes 
all cases of rays of any colour incident on transparent 
surfaces of any form and any constitution whatsoever. 
This law, therefore, includes an infinite number of cases, 
which it would have been absolutely impossible to carry 
in one's memory. Moreover, it should be noticed that 
not only does this law include the cases which we our- 
selves or other men have already observed, but that we 
shall not hesitate to apply it to new cases, not yet ob- 
served, with absolute confidence in the reliability of our 
results. In the same way, if we were to find a new species 
of mammal, not yet dissected, we are entitled to assume, 
with a confidence bordering on a certainty, that it has 
lungs, two chambers in the heart, and three or more 
tympanal bones. 

Thus, when we combine the results of experience by a 
process of thought, and form conceptions, whether general 
conceptions or laws, we not only bring our knowledge 
into a form in which it can be easily used and easily re- 
tained, but we actually enlarge it, inasmuch as we feel 
ourselves entitled to extend the rules and the laws we 
have discovered to all similar cases that may be hereafter 
presented to us. 

The above-mentioned examples are of a class in which 
the mental process of combining a number of single cases 
so as to form conceptions is unattended by farther diffi- 
culties, and can be distinctly followed in all its stages. 
But in complicated cases it is not so easy completely to 
separate like facts from unlike, and to combine them into 
a clear, well-defined conception. Assume that we know a 
man to be ambitious ; we shall perhaps be able to predict 


with tolerable certainty that if he has to act under certain 
conditions, he will follow the dictates of his ambition, 
and decide on a certain line of action. But, in the first 
place, we cannot define with absolute precision what con- 
stitutes an ambitious man, or by what standard the inten- 
sity of his ambition is to be measured ; nor, again, can we 
say precisely what degree of ambition must operate in 
order to impress the given direction on the actions of the 
man under those particular circumstances. Accordingly. 
we institute comparisons between the actions of the man 
in question, as far as we have hitherto observed them, and 
those of other men who in similar cases have acted as he 
has done, and we draw our inference respecting his future 
actions without being able to express either the major or 
the minor premiss in a clear, sharply-defined form 
perhaps even without having convinced ourselves that our 
anticipation rests on such an analogy as I have described. 
In such cases our decision proceeds only from a certain 
psychological instinct, not from conscious reasoning, 
though in reality we have gone through an intellectual 
process identical with that which leads us to assume that 
a newly-discovered mammal has lungs. 

This latter kind of induction, which can never be per- 
fectly assimilated to forms of logical reasoning, nor 
pressed so far as to establish universal laws, plays a most 
important part in human life. The whole of the process 
by which we translate our sensations into perceptions 
depends upon it, as appears especially from the investiga- 
tion of what are called illusions. For instance, when the 
retina of the eye is irritated by a blow, we imagine we 
see a light in our field of vision, because we have, 
throughout our lives, felt irritation in the optic nerves 
only when there was light in the field of vision, and have 
become accustomed to identify the sensations of those 
nerves with the presence of light in the field of vision^ 


Moreover, such is the complexity of the influences affect- 
ing the formation both of character in general and of the 
mental condition at any given moment, that this same 
kind of induction necessarily plays a leading part in the 
investigation of psychological processes. In fact, in 
ascribing to ourselves free-will, that is, full power to act 
as we please, without being subject to a stern inevitable 
law of causality, we deny in toto the possibility of re- 
ferring at least one of the ways in which our mental 
activity expresses itself to a rigorous law. 

We might possibly, in opposition to logical induction 
which reduces a question to clearly-defined universal 
propositions, call this kind of reasoning esthetic induc- 
tion, because it is most conspicuous in the higher class of 
works of art. It is an essential part of an artist's talent 
to reproduce by words, by form, by colour, or by music, 
the external indications of a character or a state of mind, 
and by a kind of instinctive intuition, uncontrolled by 
any definable rule, to seize the necessary steps by which 
we pass from one inood to another. If we do find that 
the artist has consciously worked after general rules and 
abstractions, we think his work poor and commonplace, 
and cease to admire. On the contrary, the works of 
great artists bring before us characters and moods with 
such a lifelikeness, with such a wealth of individual traits 
and such an overwhelming conviction of truth, that they 
almost seem to be more real than the reality itself, because 
all disturbing influences are eliminated. 

Now if, after these reflections, we proceed to review 
the different sciences, and to classify them according to 
the method by which they must arrive at their results, 
we are brought face to face with a generic difference 
between the natural and the moral sciences. The natural 
sciences are for the most part in a position to reduce their 
inductions to sharply-defined general rules and principles; 


the moral sciences, on the other hand, have, in by far the 
most numerous cases, to do with conclusions arrived at by 
psychological instinct. Philology, in so far as it is con- 
cerned with the interpretation and emendation of the 
texts handed down to us, must seek to feel out, as it were, 
the meaning which the author intended to express, and 
the accessory notions which he wished his words to 
suggest ; and for that purpose it is necessary to start with 
a correct insight, both into the personality of the author, 
and into the genius of the language in which he wrote. 
All this affords scope for aesthetic, but not for strictly 
logical induction. It is only possible to pass judgment, 
if you have ready in your memory a great number of 
similar facts, to be instantaneously confronted with the 
question you are trying to solve. Accordingly, one of 
the first requisites for studies of this class is an accurate 
and ready memory. Many celebrated historians and 
philologists have, in fact, astounded their contemporaries 
by their extraordinary strength of memory. Of course 
memory alone is insufficient without a knack of every- 
where discovering real resemblance, and without a deli- 
cately and fully trained insight into the springs of human 
action ; while this again is unattainable without a certain 
warmth of sympathy and an interest in observing the 
working of other men's minds. Intercourse with our 
fellow-men in daily life must lay the foundation of this 
insight, but the study of history and art serves to make 
it richer and completer, for there we see men acting 
under comparatively unusual conditions, and thus come 
to appreciate the full scope of the energies which lie 
hidden in our breasts. 

None of this group of sciences, except grammar, lead 
us, as a rule, to frame and enunciate general laws, valid 
under all circumstances. The laws of grammar are a 
product of the human will, though they can hardly be 


said to have been framed deliberately, but rather to have 
grown up gradually, as they were wanted. Accordingly, 
they present themselves to a learner rather in the form 
r,f commands, that is, of laws imposed by external au- 

With these sciences theology and jurisprudence are 
naturally connected. In fact, certain branches of history 
and philology serve both as stepping-stones and as hand- 
maids to them. The general laws of theology and juris- 
prudence are likewise commands, laws imposed by external 
authority to regulate, from a moral or juridical point of 
view, the actions of mankind ; not laws which, like those 
of nature, contain generalisations from a vast multitude 
of facts. At the same time the application of a gramma- 
tical, legal, moral, or theological rule is couched, like the 
application of a law of nature to a particular case, in the 
forms of logical inference. The rule forms the major 
premiss of the syllogism, while the minor must set lie 
whether the case in question satisfies the conditions to 
which the rule is intended to apply. The solution of this 
latter problem, whether in grammatical analysis, where 
the meaning of a sentence is to be evolved, or in the legal 
criticism of the credibility of the facts alleged, of the 
intentions of the parties, or of the meaning of the docu- 
ments they have put into court, will, in most cases, be 
again a matter of psychological insight. On the other 
hand, it should not be forgotten that both the syntax of 
fully-developed languages and a system of jurisprudence 
gradually elaborated, as ours has been, by the practice of 
more than 2,000 years, 1 have reached a high pitch of 
logical completeness and consistency ; so that, speaking 
generally, the cases which do not obviously fall under 

1 It should be remembered that the Roman law, "which has only parti- 
ally and indirectly influenced English practice, is the recognised basis of 
German jurisprudence. TB. 


some one or other of the laws actually laid down are 
quite exceptional. Such exceptions there will always be, 
for the legislation of man can never have the absolute 
consistency and perfection of the laws of nature. In 
such cases there is no course open but to try and guess 
the intention of the legislator ; or, if needs be, to 
supplement it after the analogy of his decisions in 
similar cases. 

Grammar and jurisprudence have a certain advantage 
as means of training the intellect, inasmuch as they tax 
pretty equally all the intellectual powers. On this account 
secondary education among modern European nations is 
based mainly upon the grammatical study of foreign 
languages. The mother-tongue and modern foreign lan- 
guages, when acquired solely by practice, do not call for 
any conscious logical exercise of thought, though we may 
cultivate by means of them an appreciation for artistic 
beauty of expression. The two classical languages, Latin 
and Greek, have, besides their exquisite logical subtlety 
and aesthetic beauty, an additional advantage, which they 
seem to possess in common with most ancient and original 
languages they indicate accurately the relations of words 
and sentences to each other by numerous and distinct 
inflexions. Languages are, as it were, abraded by long 
use ; grammatical distinctions are cut down to a mini- 
mum for the sake of brevity and rapidity of expression, 
and are thus made less and less definite, as is obvious from 
the comparison of any modern European language with 
Latin ; in English the process has gone further than in 
any other. This seems to me to be really the reason why 
the modern languages are far less fitted than the ancient 
for instruments of education. 1 

1 Those to whom German is not a foreign tongue may, perhaps, be per- 
mitted to hold different views on the efficacy of modern languages in 
eel ucation. TB. 


As grammar is the staple of school education, legal 
studies are used, and rightly, as a means of training per- 
sons of maturer age, even when not specially required for 
professional purposes. 

We now come to those sciences which, in respect of the 
kind of intellectual labour they require, stand at the oppo- 
site end of the series to philology and history ; namely, the 
natural and physical sciences. I do not mean to say that 
in many branches even of these sciences an instinctive 
appreciation of analogies and a certain artistic sense have 
no part to play. On the contrary, in natural history the 
decision which characteristics are to be looked upon as 
important for classification, and which as unimportant, 
what divisions of the animal and vegetable kingdoms are 
more natural than others, is really left to an instinct of 
this kind, acting without any strictly definable rule. And 
it is a very suggestive fact that it was an artist, Goethe, 
who gave the first impulse to the researches of compara- 
tive anatomy into the analogy of corresponding organs in 
different animals, and to the parallel theory of the meta- 
morphosis of leaves in the vegetable kingdom ; and thus, 
in fact, really pointed out the direction which the science 
has followed ever since. But even in those departments of 
science where we have to do with the least understood 
vital processes it is, speaking generally, far easier to 
make out general and comprehensive ideas and prin- 
ciples, and to express them in definite language, than in 
cases where we must base our judgment on the analysis of 
the human mind. It is only when we come to the experi- 
mental sciences to which mathematics are applied, and 
especially when we come to pure mathematics, that we 
see the peculiar characteristics of the natural and physical 
sciences fully brought out. 

The essential differentia of these sciences seems to me 
to consist in the comparative ease with which the indi- 


results of observation and experiment are com- 
bined under general laws of unexceptionable validity and 
of an extraordinarily comprehensive character. In the 
moral sciences, on the other hand, chis is just the point 
where insuperable difficulties are encountered. In mathe- 
matics the general propositions which, under the name of 
axioms, stand at the head of the reasoning, are so few in 
number, so comprehensive, and so immediately obvious, 
that no proof whatever is needed for them. Let me 
remind you that the whole of algebra and arithmetic is 
developed out of the three axioms : 

6 Things which are equal to the same things are equal 
to one another.' 

6 If equals be added to equals, the wholes are equal.' 
6 If unequals be added to equals, the wholes are unequal.' 
And the axioms of geometry and mechanics are not more 
numerous. The sciences we have named are developed out 
of these few axioms by a continual process of deduction 
from them in more and more complicated cases. Algebra, 
however, does not confine itself to finding the sum of the 
most heterogeneous combinations of a finite number of 
magnitudes, but in the higher analysis it teaches us to 
sum even infinite series, the terms of which increase or 
dimmish according to the most various laws ; to solve, in 
fact, problems which could never be completed by direct 
addition. An instance of this kind shows us the conscious 
logical activity of the mind in its purest and most perfect 
form. On the one hand we see the laborious nature of 
the process, the extreme caution with which it is necessary 
to advance, the accuracy required to determine exactly the 
scope of such universal principles as have been attained, 
the difficulty of forming and understanding abstract con- 
ceptions. On the other hand, we gain confidence in the 
certainty, the range, and the fertility of this kind of 
intellectual work. 


The fertility of the method comes out more strikingly 
in applied mathematics, especially in mathematical 
physics, including, of course, physical astronomy. From 
the time when Newton discovered, by analysing the 
motions of the planets on mechanical principles, that 
every paiticle of ponderable matter in the universe 
attracts every other particle with a force varying in- 
versely as the square of the distance, astronomers have 
been able, in virtue of that one law of gravitation, to 
calculate with the greatest accuracy the movements of 
the planets to the remotest past and the most distant 
future, given only the position, velocity, and mass of each 
body of our system at any one time. More than that, we 
recognise the operation of this law in the movements of 
double stars, whose distances from us are so great that 
their light takes years to reach us ; in some cases, indeed, 
so great that all attempts to measure them have failed. 

This discovery of the law of gravitation and its conse- 
quences is the most imposing achievement that the 
logical power of the human mind has hitherto per- 
formed. I do not mean to say that there have not been 
men who in power of abstraction have equalled or even 
surpassed Newton and the other astronomers, who either 
paved the way for his discovery, or have carried it out to 
its legitimate consequences ; but there has never been 
presented to the human mind such an admirable subject 
as those involved and complex movements of the planets, 
which hitherto had served merely as food for the astrolo- 
gical superstitions of ignorant star-gazers, and were now 
reduced to a single law, capable of rendering the most 
exact account of the minutest detail of their motions. 

The principles of this magnificent discovery have been 
successfully applied to several other physical sciences, 
among which physical optics and the theory of electricity 
and magnetism are especially worthy of notice. The ex- 


perimental sciences have one great advantage over the 
natural sciences in the investigation of general laws of 
nature : they can change at pleasure the conditions under 
which a given result takes place, and can thus confine 
themselves to a small number of characteristic instances, 
in order to discover the law,. Of course its validity must 
then stand the test of application to more complex cases. 
Accordingly the physical sciences, when once the right 
methods have been discovered, have made proportionately 
rapid progress. Not only have they allowed us to look 
back into primaeval chaos, where nebulous masses were 
forming themselves into suns and planets, and becom- 
ing heated by the energy of their contraction ; not only 
have they permitted us to investigate the chemical con- 
stituents of the solar atmosphere and of the remotest 
fixed stars, but they have enabled us to turn the forces of 
surrounding nature to our own uses and to make them the 
ministers of our will. 

Enough has been said to show how widely the intel- 
lectual processes involved in this group of sciences differ, 
for the most part, from those required by the moral 
sciences. The mathematician need have no memory 
whatever for detached facts, the physicist hardly any. 
Hypotheses based on the recollection of similar cases may, 
indeed, be useful to guide one into the right track, but 
they have no real value till they have led to a precise and 
strictly defined law. Nature does not allow us for a moment 
to doubt that we have to do with a rigid chain of cause 
and effect, admitting of no exceptions. Therefore to us, 
as her students, goes forth the mandate to labour on till we 
have discovered unvarying laws ; till then we dare not rest 
satisfied, for then only can our knowledge grapple victo- 
riously with time and space and the forces of the universe. 

The iron labour of conscious logical reasoning demands 
great perseverance and great caution; it moves on but 


slowly, and is rarely illuminated by brilliant flashes of 
genius. It knows little of that facility with which the 
most varied instances come thronging into the memory of 
the philologist or the historian. Rather is it an essential 
condition of the methodical progress of mathematical 
reasoning that the mind should remain concentrated on a 
single point, undisturbed alike by collateral ideas on the 
one hand, and by wishes and hopes on the other, and 
moving on steadily in the direction it has deliberately 
chosen. A celebrated logician, Mr. John Stuart Mill, 
expresses his conviction that the inductive sciences have 
of late done more for the advance of logical methods than 
the labours of philosophers properly so called. One essen- 
tial ground for such an assertion must undoubtedly be that 
in no department of knowledge can a fault in the chain of 
reasoning be so easily detected by the incorrectness of the 
results as in those sciences in which the results of reason- 
ing can be most directly compared with the facts of nature. 
Though I have maintained that it is in the physical 
sciences, and especially in such branches of them as are 
treated mathematically, that the solution of scientific 
problems has been most successfully achieved, you will 
not, I trust, imagine that I wish to depreciate other 
studies in comparison with them. If the natural and 
physical sciences have the advantage of great perfection 
in form, it is the privilege of the moral sciences to deal 
with a richer material, with questions that touch more 
nearly the interests and the feelings of men, with the 
human mind itself, in fact, in its motives and the 
different branches of its activity. They have, indeed, 
the loftier and the more difficult task, but yet they 
cannot afford to lose sight of the example of their rivals, 
which, in form at least, have, owing to the more ductile 
nature of their materials, made greater progress. Not 
only have they something to learn from them in point of 


method, but they may also draw encouragement from 
the greatness of their results. And I do think that our 
age has learnt many lessons from the physical sciences. 
The absolute, unconditional reverence for facts, and the 
fidelity with which they are collected, a certain distrust- 
fulness of appearances, the effort to detect in all cases 
relations of cause and effect, and the tendency to assume 
their existence, which distinguish our century from pre- 
ceding ones, seem to me to point to such an influence. 

I do not intend to go deeply into the question how 
far mathematical studies, as the representatives of con- 
scious logical reasoning, should take a more important 
place in school education. But it is, in reality, one of 
the questions of the day. In proportion as the range of 
science extends, its system and organisation must be 
improved, and it must inevitably come about that in- 
dividual students will find themselves compelled to go 
through a stricter course of training than grammar is in 
a position to supply. What strikes me in my own ex- 
perience of students who pass from our classical schools 
to scientific and medical studies, is first, a certain laxity 
in the application of strictly universal laws. The gram- 
matical rules, in which they have been exercised, are 
for the most part followed by long lists of exceptions ; 
accordingly they are not in the habit of relying implicitly 
on the certainty of a legitimate deduction from a strictly 
universal law. Secondly, I find them for the most part 
too much inclined to trust to authority, even in cases 
where they might form an independent judgment. In 
fact, in philological studies, inasmuch as it is seldom 
possible to take in the whole of the premisses at a glance, 
and inasmuch as the decision of disputed questions often 
depends on an aesthetic feeling for beauty of expres- 
sion, and for the genius of the language, attainable 
only by long training, it must often happen that the 


student is referred to authorities even by the best 
teachers. Both faults are traceable to a certain in- 
dolence and vagueness of thought, the sad effects of 
which are not confined to subsequent scientific studies. 
"Rut certainly the best remedy for both is to be found in 
mathematics, where there is absolute certainty in the 
reasoning, and no authority is recognised but that of 
one's own intelligence. 

So much for the several branches of science considered 
as exercises for the intellect, and as supplementing each 
other in that respect. But knowledge is not the sole 
object of man upon earth. Though the sciences arouse 
and educate the subtlest powers of the mind, yet a man 
who should study simply for the sake of knowing, would 
assuredly not fulfil the purpose of his existence. We 
often see men of considerable endowments, to whom 
their good or bad fortune has secured a comfortable 
livelihood or good social position, without giving them, 
at the same time, ambition or energy enough to make 
them work, dragging out a weary, unsatisfied existence, 
while all the time they fancy they are following the 
noblest aim of life by constantly devoting themselves to 
the increase of their knowledge, and the cultivation of 
their minds. Action alone gives a man a life worth 
living ; and therefore he must aim either at the practical 
application of his knowledge, or at the extension of the 
limits of science itself. For to extend the limits of science 
is really tp work for the progress of humanity. Thus we 
pass to the second link, uniting the different sciences, 
the connection, namely, between the subjects of which 
they treat. 

Knowledge is power. Our age, more than any other, 
is in a position to demonstrate the truth of this maxim. 
We have taught the forces of inanimate nature to 
minister to the wants of human life and the designs of 


the human intellect. The application of steam has 
multiplied our physical strength a million-fold ; weaving 
and spinning machines have relieved us of labours, the 
only merit of which consisted in a deadening monotony. 
The intercourse between men, with its far-reaching in- 
fluence on material and intellectual progress, has increased 
to an extent of which no one could have even dreamed 
within the lifetime of the older among us. But it is not 
merely on the machines by which our powers are multi- 
plied; not merely on rifled cannon, and armour-plated 
ships ; not merely on accumulated stores of money and 
the necessaries of life, that the power of a nation rests ; 
though these things have exercised so unmistakeable an 
influence, that even the proudest and most obstinate 
despotisms of our times have been forced to think of 
removing restrictions on industry, and of conceding to 
the industrious middle classes a due voice in their 
counsels. But political organisation, the administration 
of justice, and the moral discipline of individual citizens 
are no less important conditions of the preponderance of 
civilised nations ; and so surely as a nation remains in- 
accessible to the influences of civilisation in these respects, 
so surely is it on the high road to destruction. The 
several conditions of national prosperity act and react on 
each other ; where the administration of justice is uncer- 
tain, where the interests of the majority cannot be asserted 
by legitimate means, the development of the national 
resources, and of the power depending upon them, is 
impossible ; nor again, is it possible to make good soldiers 
except out of men who have learnt under just laws to 
educate the sense of honour that characterises an inde- 
pendent man, certainly not out of those who have lived 
the submissive slaves of a capricious tyrant. 

Accordingly every nation is interested in the progress 
of knowledge on the simple ground of self-preservation. 


even were there no higher wants of an ideal character to 
be satisfied ; and not merely in the development of the 
physical sciences, and their technical application, but 
also in the progress of legal, political, and moral sciences, 
and of the accessory historical and philological studies. 
No nation which would be independent and influential 
can afford to be left behind in the race. Nor has this 
escaped the notice of the cultivated peoples of Europe. 
Never before was so large a part of the public resources 
devoted to universities, schools, and scientific institutions. 
We in Heidelberg have this year occasion to congratu- 
late ourselves on another rich endowment granted by our 
government and our parliament. 

I was speaking, at the beginning of my address, of the 
increasing division of labour and the improved organisa- 
tion among scientific workers. In fact, men of science 
form, as it were, an organised army, labouring on behalf 
of the whole nation, and generally under its direction 
and at its expense, to augment the stock of such know- 
ledge as may serve to promote industrial enterprise, to 
increase wealth, to adorn life, to improve political and 
social relations, and to further the moral development of 
individual citizens. After the immediate practical re- 
sults of their work we forbear to inquire ; that we leave 
to the uninstructed. We are convinced that whatever 
contributes to the knowledge of the forces of nature or 
the powers of the human mind is worth cherishing, and 
may, in its own due time, bear practical fruit, very often 
where we should least have expected it. Who, when 
Gralvani touched the muscles of a frog with different 
metals, and noticed their contraction, could have dreamt 
that eighty years afterwards, in virtue of the self-same 
process, whose earliest manifestations attracted his at- 
tention in his anatomical researches, all Europe would 
be traversed with wires, flashing intelligence from Madrid 


to St. Petersburg with the speed of lightning ? In the 
hands of Gralvani, and at first even in Volta's, electrical 
currents were phenomena capable of exerting only the 
feeblest forces, and could not be detected except by the 
most delicate apparatus. Had they been neglected, on 
the ground that the investigation of them promised no 
immediate practical result, we should now be ignorant of 
the most important and most interesting of the links 
between the various forces of nature. When young 
Galileo, then a student at Pisa, noticed one day during 
divine service a chandelier swinging backwards and for- 
wards, and convinced himself, by counting his pulse, that 
the duration of the oscillations was independent of the 
arc through which it moved, who could know that this 
discovery would eventually put it in our power, by means 
of the pendulum, to attain an accuracy in the measure- 
ment of time till then deemed impossible, and would 
enable the storm-tossed seaman in the most distant oceans 
to determine in what degree of longitude he was sailing ? 
Whoever, in the pursuit of science, seeks after imme- 
diate practical utility, may generally rest assured that he 
will seek in vain. All that science can achieve is a perfect 
knowledge and a perfect understanding of the action of 
natural and moral forces. Each individual student must 
be content to find his reward in rejoicing over new dis- 
coveries, as over new victories of mind over reluctant 
matter, or in enjoying the aesthetic beauty of a well- 
ordered field of knowledge, where the connection and the 
filiation of every detail is clear to the mind, and where all 
denotes the presence of a ruling intellect ; he must rest 
satisfied with the consciousness that he too has contributed 
something to the increasing fund of knowledge on which 
the dominion of man over all the forces hostile to intelli- 
gence reposes. He will, indeed, not always be permitted 
to expect from his fellow-men appreciation and reward 


adequate to the value of his work. It is only too true, 
that many a man to whom a monument has been erected 
after his death, would have been delighted to receive 
during his lifetime a tenth part of the money spent in 
doing honour to his memory. At the same time, we must 
acknowledge that the value of scientific discoveries is now 
far more fully recognised than formerly by public opinion, 
and that instances of the authors of great advances in 
science starving in obscurity have become rarer and rarer. 
On the contrary, the governments and peoples of Europe 
have, as a rule, admitted it to be their duty to recompense 
distinguished achievements in science by appropriate ap- 
pointments or special rewards. 

The sciences have then, in this respect, all one common 
aim, to establish the supremacy of intelligence over the 
world : while the moral sciences aim directly at making 
the resources of intellectual life more abundant and more 
interesting, and seek to separate the pure gold of Truth 
from alloy, the physical sciences are striving indirectly 
towards the same goal, inasmuch as they labour to make 
mankind more and more independent of the material re- 
straints that fetter their activity. Each student works in 
his own department, he chooses for himself those tasks for 
which he is best fitted by his abilities and his training. 
But each one must be convinced that it is only in connec- 
tion with others that he can further the great work, and 
that therefore he is bound, not only to investigate, but to 
do his utmost to make the results of his investigation 
completely and easily accessible. If he does this, he will 
derive assistance from others, and will in his turn be able 
to render them his aid. The annals of science abound in 
evidence how such mutual services have been exchanged, 
even between departments of science apparently most 
remote. Historical chronology is essentially based on 
astronomical calculations of eclipses, accounts of which 


are preserved in ancient histories. Conversely, many of 
the important data of astronomy for instance, the in- 
variability of the length of the day, and the periods of 
several comets rest upon ancient historical notices. Of 
late years, physiologists, especially Briicke, have actually 
undertaken to draw up a complete system of all the 
vocables that can be produced by the organs of speech, 
and to base upon it propositions for an universal alphabet, 
adapted to all human languages. Thus physiology has 
entered the service of comparative philology, and has 
already succeeded in accounting for many apparently 
anomalous substitutions, on the ground that they are 
governed, not as hitherto supposed, by the laws of eu- 
phony, but by similarity between the movements of the 
mouth that produce them. Again, comparative philo- 
logy gives us information about the relationships, the 
separations and the migrations of tribes in prehistoric 
times, and of the degree of civilisation which they had 
reached at the time when they parted. For the names of 
objects to which they had already learnt to give distinc- 
tive appellations reappear as words common to their later 
languages. So that the study of languages actually gives 
us historical data for periods respecting which no other 
historical evidence exists. 1 Yet again I may notice the 
help which not only the sculptor, but the archaeologist, 
concerned with the investigation of ancient statues, 
derives from anatomy. And if I may be permitted to 
refer to my own most recent studies, I would mentionl 
that it is possible, by reference to physical acoustics) 
and to the physiological theory of the sensation of hear-/ 
ing, to account for the elementary principles on which 
our musical system is constructed, a problem essentially 
within the sphere of aesthetics. In fact, it is a general 
principle that the physiology of the organs of sense is 
1 See, for example, Mommsen's Rome, Book I. ch. ii. Tn. 


most intimately connected with psychology, inasmuch as 
physiology traces in our sensations the results of mental 
processes which do not fall within the sphere of con- 
ciousness, and must therefore have remained inaccessible 
to us. 

I have been able to quote only some of the most 
striking instances of this interdependence of different 
sciences, and such as could be explained in a few words. 
Naturally, too, I have tried to choose them from the most 
widely-separated sciences. But far wider is of course the 
influence which allied sciences exert upon each other. 
Of that I need not speak, for each of you knows it from 
his own experience. 

In conclusion, I would say, let each of us think of him- 
self, not as a man seeking to gratify his own thirst for 
knowledge, or to promote his own private advantage, or 
to shine by his own abilities, but rather as a fellow- 
labourer in one great common work bearing upon the 
highest interests of humanity. Then assuredly we shall 
not fail of our reward in the approval of our own con- 
science and the esteem of our fellow-citizens. To keep 
up these relations between all searchers after truth and 
all branches of knowledge, to animate them all to vigo- 
rous co-operation towards their common end, is the great 
office of the Universities. Therefore is it necessary that 
the four Faculties should ever go hand in hand, and in 
this conviction will we strive, so far as in us lies, to press 
onward to the fulfilment of our great mission. 




IT could not but be that Goethe, whose comprehensive 
genius was most strikingly apparent in that sober clear- 
ness with which he grasped and reproduced with lifelike 
freshness the realities of nature and human life in their 
minutest details, should, by those very qualities of his 
mind, be drawn towards the study of physical science. 
And in that department, he was not content with ac- 
quiring what others could teach him, but he soon at- 
tempted, as so original a mind was sure to do, to strike 
out an independent and a very characteristic line of 
thought. He directed his energies, not only to the 
descriptive, but also to the experimental sciences ; the 
chief results being his botanical and osteological treatises 
on the one hand, and his theory of colour on the other. 
The first germs of these researches belong for the most 
part to the last decade of the eighteenth century, though 
some of them were not completed nor published till later. 
Since that time science has not only made great progress, 
but has widely extended its range. It has assumed in 
some respects an entirely new aspect, it has opened out 


new fields of research and undergone many changes in its 
theoretical views. I shall attempt in the following 
Lecture to sketch the relation of Goethe's researches to 
the present stand-point of science, and to bring out the 
guiding idea that is common to them all. 

The peculiar character of the descriptive sciences 
botany, zoology, anatomy, and the like is a necessary 
result of the work imposed upon them. They undertake 
to collect and sift an enormous mass of facts, and, above 
all, to bring them into a logical order or system. Up to 
this point their work is only the dry task of a lexico- 
grapher ; their system is nothing more than a muniment- 
room in which the accumulation of papers is so arranged 
that any one can find what he wants at any moment. 
The more intellectual part of their work and their real 
interest only begins when they attempt to feel after the 
scattered traces of law and order in the disjointed, hetero- 
geneous mass, and out of it to construct for themselves an 
orderly system, accessible at a glance, in which every 
detail has its due place, and gains additional interest from 
its connection with the whole. 

In such studies, both the organising capacity and the 
insight of our poet found a congenial sphere the epoch 
was moreover propitious to him. He found ready to 
his hand a sufficient store of logically arranged mate- 
rials in botany and comparative anatomy, copious and 
systematic enough to admit of a comprehensive view, 
and to indicate the way to some happy glimpse of an 
all-pervading law ; while his contemporaries, if they made 
any efforts in this direction, wandered without a com- 
pass, or else they were so absorbed in the dry registra- 
tion of facts, that they scarcely ventured to think of 
anything beyond. It was reserved for Goethe to intro- 
duce two ideas of infinite fruitfulness. 

The first was the conception that the difference:? in the 


anatomy of different animals are to be looked upon as 
variations from a common phase or type, induced by dif- 
ferences of habit, locality, or food. The observation 
which led him to this fertile conception was by no means 
a striking one ; it is to be found in a monograph on the 
intermaxillary bone, written as early as 1786. It was 
known that in most vertebrate animals (that is, mam- 
malia, birds, amphibia, and fishes) the upper jaw consists 
of two bones, the upper jaw-bone and the intermaxillary 
bone. The former always contains in the mammalia the 
molar and the canine teeth, the latter the incisors. Man, 
who is distinguished from all other animals by the ab- 
sence of the projecting snout, has, on the contrary, on 
each side only one bone, the upper jaw-bone, containing 
all the teeth. This being so, Groethe discovered in the 
human skull faint traces of the sutures, which in animals 
unite the upper and middle jaw-bones, and concluded 
from it that man had originally possessed an inter- 
maxillary bone, which had subsequently coalesced with 
the upper jaw-bone. This obscure fact opened up to him 
a source of the most intense interest in the field of osteo- 
logy, generally so much decried as the driest of studies. 
That details of structure should be the same in man and 
in animals when the parts continue to perform similar 
functions had involved nothing extraordinary. In fact, 
Camper had already attempted, on this principle, to trace 
similarities of structure even between man and fishes. 
But the persistence of this similarity, at least in a rudi- 
mentary form, even in a case when it evidently does not 
correspond to any of the requirements of the complete 
human structure, and consequently needs to be adapted 
to them by the coalescence of two parts originally sepa- 
rate, was what struck Groethe's far-seeing eye, and sug- 
gested to him a far more comprehensive view than had 
hitherto been taken. Further studies soon convinced 


him of the universality of his newly-discovered principle, 
so that in 1795 and 1796 he was able to define more 
clearly the idea that had struck him in 1786, and to 
commit it to writing in his ' Sketch of a General Intro- 
duction to Comparative Anatomy.' He there lays down 
with the utmost confidence and precision, that all differ- 
ences in the structure of animals must be looked upon as 
variations of a single primitive type, induced by the 
coalescence, the alteration, the increase, the diminution, 
or even the complete removal of single parts of the 
structure ; the very principle, in fact, which has become 
the leading idea of comparative anatomy in its present 
stage. Nowhere has it been better or more clearly ex- 
pressed than in Goethe's writings. Subsequent authorities 
have made but few essential alterations in his theory. 
The most important of these is, that we no longer under- 
take to construct a common type for the whole animal 
kingdom, but are content with one for each of Cuvier's 
great divisions. The industry of Goethe's successors has 
accumulated a well-sifted stock of facts, infinitely more 
copious than what he could command, and has followed 
up successfully into the minutest details what he could 
only indicate in a general way. 

The second leading conception which science owes to 
Goethe enunciated the existence of an analogy between 
the different parts of one and the same organic being, 
similar to that which we have just pointed out as sub- 
sisting between corresponding parts of different species. 
In most organisms we see a great repetition of single 
parts. This is most striking in the vegetable kingdom ; 
each plant has a great number of similar stem leaves, 
similar petals, similar stamens, and so on. According to 
Goethe's own account, the idea first occurred to him while 
looking at a fan-palm at Padua. He was struck by the 
immense variety of changes of form which the sue- 


cessively-developed stem-leaves exhibit, by the way in 
which the first simple root leaflets are replaced by a series 
of more and more divided leaves, till we come to the most 

He afterwards succeeded in discovering the transforma- 
tion of stem-leaves into sepals and petals, and of sepals 
and petals into stamens, nectaries, and ovaries, and thus 
he was led to the doctrine of the metamorphosis of plants, 
which he published in 1790. Just as the anterior extre- 
mity of vertebrate animals takes different forms, becoming 
in man and in apes an arm, in other animals a paw with 
claws, or a forefoot with a hoof, or a fin, or a wing, but 
always retains the same divisions, the same position, and 
the same connection with the trunk, so the leaf appears 
as a cotyledon, stem-leaf, sepal, petal, stamen, nectary, 
ovary, &c., all resembling each other to a certain extent 
in origin and composition, and even capable, under 
certain unusual conditions, of passing from one form into 
the other, as, for example, may be seen by any one who 
looks carefully at a full-blown rose, where some of the 
stamens are completely, some of them partially, changed 
into petals. This view of Groethe's, like the other, is now 
completely adopted into science, and enjoys the universal 
assent of botanists, though of course some details are still 
matters of controversy, as, for instance, whether the bud 
is a single leaf or a branch. 

In the animal kingdom, the composition of an indi- 
vidual out of several similar parts is very striking in the 
great sub-kingdom of the articulata for example, in 
insects and worms. The larva of an insect, or the cater- 
pillar of a butterfly, consists of a number of perfectly 
similar segments ; only the first and last of them differ, 
and that but slightly, from the others. After their 
transformation into perfect insects, they furnish clear and 
simple exemplifications of the view which Goethe had 


grasped in his doctrine of the metamorphosis of plants, 
the development, namely, of apparently very dissimilar 
forms from parts originally alike. The posterior seg- 
ments retain their original simple form ; those of the 
breast-plate are drawn closely together, and develop feet 
and wings ; while those of the head develop jaws and 
feelers ; so that in the perfect insect, the original seg~ 
\ ments are recognised only in the posterior part of the 
body. In the vertebrata, again, a repetition of similar 
parts is suggested by the vertebral column, but has ceased 
to be observable in the external form. A fortunate glance 
at a broken sheep's skull, which Groethe found by acci- 
dent on the sand of the Li do at Venice, suggested to him 
that the skull itself consisted of a series of very much 
altered vertebrae. At first sight, no two things can be 
more unlike than the broad uniform cranial cavity of the 
mammalia, inclosed by smooth plates, and the narrow 
cylindrical tube of the spinal marrow, composed of short, 
massy, jagged bones. It was a bright idea to detect the 
transformation in the skull of a mammal ; the similarity 
is more striking in the amphibia and fishes. It should 
be added that Groethe left this idea unpublished for a 
long time, apparently because he was not quite sure how 
it would be received. Meantime, in 1806, the same idea 
occurred to Oken, who introduced it to the scientific 
world, and afterwards disputed with Groethe the priority 
of discovery. In fact, Groethe had waited till 1817, when 
the opinion had begun to find adherents, and then de- 
clared that he had had it in his mind for thirty years. 
Up to the present day, the number and composition of 
the vertebrae of the skull are a subject of controversy, 
but the principle has maintained its ground. 

Groethe's views, however, on the existence of a common 
type in the animal kingdom do not seem to have exercised 
any direct influence on the progress of science. The 


doctrine of the metamorphosis of plants was introduced 
into botany as his distinct and recognised property ; but 
his views on osteology were at first disputed by ana- 
tomists, and only subsequently attracted attention when 
the science had, apparently on independent grounds, 
found its way to the same discovery. He himself com- 
plains that his first ideas of a common type had en- 
countered nothing but contradiction and scepticism at 
the time when he was working them out in his own mind, 
and that even men of the freshest and most original 
intellect, like the two Von Humboldts, had listened to 
them with something like impatience. But it is almost 
a matter of course that in any natural or physical science, 
theoretical ideas attract the attention of its cultivators 
only when they are advanced in connection with the 
whole of the evidence on which they rest, and thus justify 
their title to recognition. Be that as it may, Goethe is 
entitled to the credit of having caught the first glimpse 
of the guiding ideas to which the sciences of botany and 
anatomy were tending, and by whreh their present form 
is determined. 

But great as is the respect which Groethe has secured 
by his achievements in the descriptive natural sciences, 
the denunciation heaped by all physicists on his re- 
searches in their department, and especially on his 
* theory of colour,' is at least as uncompromising. This 
is not the place to plunge into the controversy that 
raged on the subject, and so I shall only attempt to state 
clearly the points at issue, and to explain what prin- 
ciple was involved, and what is the latent significance 
of the dispute. 

To this end it is of some importance to go back to the 
history of the origin of the theory, and to its simplest 
form, because at that stage of the controversy the 
points at issue are obvious, and admit of easy and dis- 


fcinct statement, unencumbered by disputes about the 
correctness of detached facts and complicated theories. 

Groethe himself describes very gracefully, in the con- 
fession at the end of his * Theory of Colour,' how he came 
to take up the subject. Finding himself unable to grasp 
the sesthetic principles involved in effects of colour, he 
resolved to resume the study of the physical theory, which 
he had been taught at the university, and to repeat for 
himself the experiments connected with it. With that 
view he borrowed a prism of Hofrath Butter, of Jena, but 
was prevented by other occupations from carrying out his 
plan, and kept it by him for a long time unused. The 
owner of the prism, a very orderly man, after several 
times asking in vain, sent a messenger with instructions 
to bring it back directly. Goethe took it out of the case, 
and thought he would take one more peep through it. To 
make certain of seeing something, he turned it towards a 
long white wall, under the impression that as there was 
plenty of light there he could not fail to see a brilliant 
example of the resolution of light into different colours ; 
a supposition, by the way, which shows how little Newton's 
theory of the phenomena was then present to his mind. 
Of course he was disappointed. On the white wall he saw 
no colours ; they only appeared where it was bounded by 
darker objects. Accordingly he made the observation 
which, it should be added, is fully accounted for by 
Newton's theory that colour can only be seen through a 
prism where a dark object and a bright one have the same 
boundary. Struck by this observation, which was quite 
new to him, and convinced that it was irreconcilable with 
Newton's theory, he induced the owner of the prism to 
relent, and devoted himself to the question with the 
utmost zeal and interest. He prepared sheets of paper 
with black and white spaces, and studied the phenomenon 
urder every variety of condition, until he thought he had 


sufficiently proved his rules. He next attempted to ex- 
plain his supposed discovery to a neighbour, who was a 
physicist, and was disagreeably surprised to be assured by 
him that the experiments were well known, and fully 
accounted for in Newton's theory. Every other natural 
philosopher whom he consulted told him exactly the same, 
including even the brilliant Lichtenberg, whom he tried 
for a long time to convert, but in vain. He studied 
Newton's writings, and fancied he had found some falla- 
cies in them which accounted for the error. Unable to 
convince any of his acquaintances, he at last resolved to 
appear before the bar of public opinion, and in 1791 and 
1792 published the first and second parts of his 'Contri- 
butions to Physical Optics.' 

In that work he describes the appearances presented by 
white discs on a black ground, black discs on a white 
ground, and coloured discs on a black or white ground, 
when examined through a prism. As to the results of 
the experiments there is no dispute whatever between him 
and the physicists. He describes the phenomena he saw 
with great truth to nature ; the style is lively, and the 
arrangement such as to make a conspectus of them easy 
and inviting ; in short, in this as in all other cases where 
facts are to be described, he proves himself a master. At 
the same time he expresses his conviction that the facts 
lie has adduced are calculated to refute Newton's theory. 
There are two points especially which he considers fatal to 
it : first, that the centre of a broad white surface remains 
white when seen through a prism ; and secondly, that 
even a black streak on a white ground can be entirely 
decomposed into colours. 

Newton's theory is based on the hypothesis that there 
exists light of different kinds, distinguished from one 
another by the sensation of colour which they produce in 
the eye. Thus there is red, orange, yellow, green, blue, 


and violet light, and light of ail intermediate colours. 
Different kinds of light, or differently coloured lights, 
produce, when mixed, derived colours, which to a cer- 
tain extent resemble the original colours from which 
they are derived ; to a certain extent form new 
tints. White is a mixture of all the before-named 
colours in certain definite proportions. But the pri- 
mitive colours can always be reproduced by analysis 
from derived colours, or from white, while themselves 
incapable of analysis or change. The cause of the colours 
of transparent and opaque bodies is, that when white light 
falls upon them they destroy some of its constituents and 
send to the eye other constituents, but no longer mixed 
in the right proportions to produce white light. Thus a 
piece of red glass looks red, because it transmits only red 
rays. Consequently all colour is derived solely from a 
change in the proportions in which light is mixed, and is, 
therefore, a property of light, not of the coloured bodies, 
which only furnish an occasion for its manifestation. 

A prism refracts transmitted light ; that is to say, de- 
flects it so that it makes a certain angle with its original 
direction ; the rays of simple light of different colours 
have, according to Newton, different refrangibilities, and 
therefore, after refraction in the prism, pursue different 
courses and separate from each other. Accordingly a 
luminous point of infinitely small dimensions appears, 
when seen through the prism, to be first displaced, and 
secondly, extended into a coloured line, the so-called 
prismatic spectrum, which shows what are called the pri- 
mary colours in the order above-named. If, however, you 
look at a broader luminous surface, the spectra of the 
points near the middle are superposed, as may be seen 
from a simple geometrical investigation, in such pro- 
portions as to give white light, except at the edges, where 
certain of the colours are free. This white surface appears 
displaced, as the luminous point did ; but instead of being 


coloured throughout, it has on one side a^ margin of blue 
and violet, on the other a margin of red and yellow. A 
black patch between two bright surfaces may be entirely 
covered by their coloured edges ; and when these spectra 
meet in the middle, the red of the one and the violet of 
the other combine to form purple. Thus the colours into 
which, at first sight, it seems as if the black were analysed 
are in reality due, not to the black strip, but to the white 
on each side of it. 

It is evident that at the first moment Goethe did not 
recollect Newton's theory well enough to be able to find 
out the physical explanation of the facts I have just 
glanced at. It was afterwards laid before him again and 
again, and that in a thoroughly intelligible form, for he 
speaks about it several times in terms that show he under- 
stood it quite correctly. But he is still so dissatisfied with 
it, that he persists in his assertion that the facts just cited 
are of a nature to convince any one who observes them of 
the absolute incorrectness of Newton's theory. Neither 
here nor in his later controversial writings does he ever 
clearly state in what he conceives the insufficiency of the 
explanation to consist. He merely repeats again and again 
that it is quite absurd. And yet I cannot see how any one, 
whatever his views about colour, can deny that the theory 
is perfectly consistent with itself; and that if the hypo- 
thesis from which it starts be granted, it explains the 
observed facts completely and even simply. Newton him- 
self mentions these spurious spectra in several passages of 
his optical works, without going into any special eluci- 
dation of the point, considering, of course, that the 
explanation follows at once from his hypothesis. And he 
seems to have had good reason to think so ; for Goethe no 
sooner began to call the attention of his scientific friends 
to the phenomena, than all with one accord, as he himself 
tells us, met his difficulties with this explanation from 
Newton's principles, which, though not actually in MS 


writings, instantly suggested itself to every one who knew 

A reader who tries to realise attentively and thoroughly 
every step in this part of the controversy is apt to expe- 
rience at this point an uncomfortable, almost a painful 
feeling to see a man of extraordinary abilities persist- 
ently declaring that there is an obvious absurdity lurking 
in a few inferences apparently quite clear and simple. 
He searches and searches, and at last unable, with 
all his efforts, to find any such absurdity, or even the 
appearance of it, he gets into a state of mind in which 
his own ideas are, so to speak, crystallised. But it is just 
this obvious, flat contradiction that makes Groethe's point 
of view in 1792 so interesting and so important. At this 
point he has not as yet developed any theory of his own ; 
there is nothing under discussion but a few easily-grasped 
facts, as to the correctness of which both parties are agreed, 
and yet both hold distinctly opposite views ; neither 
of them even understands what his opponent is driving 
at. On the one side are a number of physicists, who, 
by a long series of the ablest investigations, the most 
elaborate calculations, and the most ingenious inven- 
tions, have brought optics to such perfection, that it, 
and it alone, among the physical sciences, was begin- 
ning almost to rival astronomy in accuracy. Some of 
them have made the phenomena the subject of direct in- 
vestigation ; all of them, thanks to the accuracy with 
which it is possible to calculate beforehand the result 
of every variety in the construction and combination of 
instruments, have had the opportunity of putting the 
inferences deduced from Newton's views to the test of 
experiment, and all, without exception, agree in ac- 
cepting them. On the other side is a man whose 
remarkable mental endowments, and whose singular 
talent for seeing through whatever obscures reality, we 


have had occasion to recognise, not only in poetry, but 
also in the descriptive parts of the natural sciences ; and 
this man assures us with the utmost zeal that the physicists 
are wrong : he is so convinced of the correctness of his own 
view, that he cannot explain the contradiction except by 
assuming narrowness or malice on their part, and finally 
declares that he cannot help looking upon his own achieve- 
ment in the theoiy of colour as far more valuable than 
anything he has accomplished in poetry. 1 

So flat a contradiction leads us to suspect that there 
must be behind some deeper antagonism of principle, 
some difference of organisation between his mind and 
theirs, to prevent them from understanding each other. 
I will try to indicate in the following pages what I con- 
ceive to be the grounds of this antagonism. 

Goethe, though he exercised his powers in many spheres 
of intellectual activity, is nevertheless, par excellence, 
a poet. Now in poetry, as in every other art, the essen- 
tial thing is to make the material of the art, be it words, 
or music, or colour, the direct vehicle of an idea. In a 
perfect work of art, the idea must be present and domi- 
nate the whole, almost unknown to the poet himself, not 
as the result of a long intellectual process, but as inspired 
by a direct intuition of the inner eye, or by an outburst of 
excited feeling. 

An idea thus embodied in a work of art, and dressed 
in the garb of reality, does indeed make a vivid im- 
pression by appealing directly to the senses, but loses, of 
course, that universality and that intelligibility which it 
would have had if presented in the form of an abstract 
notion. The poet, feeling how the charm of his works is 
involved in an intellectual process of this type, seeks to 
apply it to other materials. Instead of trying to arrange 
the phenomena of nature under definite conceptions, in- 

1 See Eckermann's Conversations. 


dependent of intuition, he sits down to contemplate them 
as he would a work of art, complete in itself, and certain to 
yield up its central idea, sooner or later, to a sufficiently 
susceptible student. Accordingly, when he sees the skull on 
the Lido, which suggests to him the vertebral theory of 
the cranium, he remarks that it serves to revive his old 
belief, already confirmed by experience, that Nature has 
no secrets from the attentive observer. So again in his 
first conversation with Schiller on the ' Metamorphosis of 
Plants.' To Schiller, as a follower of Kant, the idea is 
the goal, ever to be sought, but ever unattainable, and 
therefore never to be exhibited as realised in a phenome- 
non. Goethe, on the other hand, as a genuine poet, 
conceives that he finds in the phenomenon the direct 
expression of the idea. He himself tells us that nothing 
brought out more sharply the separation between himself 
and Schiller. This, too, is the secret of his affinity with 
the natural philosophy of Schelling and Hegel, which 
likewise proceeds from the assumption that Nature shows 
us by direct intuition the several steps by which a con- 
ception is developed. Hence, too, the ardour with which 
Hegel and his school defended Goethe's scientific views. 
Moreover this view of Nature accounts for the war which 
Goethe continued to wage against complicated experi- 
mental researches. Just as a genuine work of art cannot 
bear retouching by a strange hand, so he would have us 
believe Nature resists the interference of the experimenter 
who tortures her and disturbs her ; and in revenge, mis- 
leads the impertinent kill-joy by a distorted image of 

Accordingly, in his attack upon Newton he often 
sneers at spectra, tortured through a number of narrow 
slits and glasses, and commends the experiments that can 
be made in the open air under a bright sun, not merely 
as particularly easy and particularly enchanting, but also 


as particularly convincing ! The poetic turn of mind is 
very marked even in his morphological researches. If 
we only examine what has really been accomplished by 
the help of the ideas which he contributed to science, 
we shall be struck by the very singular relation which 
they bear to it. No one will refuse to be convinced if 
you lay before him the series of transformations by which 
a leaf passes into a stamen, an arm into a fin or a wing, 
a vertebra into the occipital bone. The idea that all 
the parts of a flower are modified leaves, reveals a con- 
necting law, which surprises us into acquiescence. But 
now try and define the leaf-like organ, determine its 
essential characteristics, so as to include all the forms 
that we have named. You will find yourself in a diffi- 
culty, for all distinctive marks vanish, and you have 
nothing left, except that a leaf in the wider sense of the 
term is a lateral appendage of the axis of a plant. Try 
then to express the proposition ' the parts of the flower 
are modified leaves' in the language of scientific defi- 
nition, and it reads, 6 the parts of the flower are lateral 
appendages of the axis.' To see this does not require a 
Groethe. So again it has been objected, and not unjustly, 
to the vertebral theory, that it must extend the notion of 
a vertebra so much that nothing is left but the bare fact 
a vertebra is a bone. We are equally perplexed if we 
try to express in clear scientific language what we mean 
by saying that such and such a part of one animal 
corresponds to such and such a part of another. We do 
not mean that their physiological use is the same, for the 
same piece which in a bird serves as the lower jaw, 
becomes in mammals a tiny tympanal bone. Nor would 
the shape, the position, or the connection of the part in 
question with other parts, serve to identify it in all cases. 
But yet it has been found possible in most cases, by 
following the intermediate steps, to determine with toler- 


able certainty which parts correspond to each other. 
Groethe himself said this very clearly : he says, in speaking 
of the vertebral theory of the skull, c Such an aper^u^ 
such an intuition, conception, representation, notion, idea, 
or whatever you choose to call it, always retains some- 
thing esoteric and indefinable, struggle as you will 
against it ; as a general principle, it may be enunciated, 
but cannot be proved; in detail it may be exhibited, 
but can never be put in a cut and dry form.' And so, or 
nearly so, the problem stands to this day. The difference 
may be brought out still more clearly if we consider 
how physiology, which investigates the relations of vital 
processes as cause and effect, would have to treat this 
idea of a common type of animal structure. The science 
might ask. Is it, on the one hand, a correct view, that 
during the geological periods that have passed over the 
earth, one species has been developed from another, so 
that, for example, the breast-fin of the fish has gradually 
changed into an arm or a wing? Or again, shall we 
say that the different species of animals were created 
equally perfect that the points of resemblance between 
them are to be ascribed to the fact, that in all vertebrate 
animals the first steps in development from the egg can 
only be effected by Nature in one way, almost identical 
in all cases, and that the later analogies of structure are 
determined by these features, common to all embryos ? 
Probably the majority of observers incline to the latter 
view, 1 for the agreement between the embryos of dif- 
ferent vertebrate animals, in the earlier stages, is very 
striking. Thus even young mammals have occasionally 
rudimentary gills on the side of the neck, like fishes. 
It seems, in fact, that what are in the mature animals 
corresponding parts, originate in the same way during 
the process of development, so the scientific men have 
1 This was written before the appearance of Darwin's Origin of Specie*. 


lately begun to make use of embryology as a sort of 
check on the theoretical views of comparative anatomy. 
It is evident that by the application of the physiological 
views just suggested, the idea of a common type would 
acquire definiteness and meaning as a distinct scientific 
conception. Goethe did much : he saw by a happy 
intuition that there was a law, and he followed up the 
indications of it with great shrewdness. But what law 
it was, he did not see ; nor did he even try to find it out. 
That was not in his line. Moreover, even in the present 
condition of science, a definite view on the question is 
impossible ; the very form in which it should be proposed 
is scarcely yet settled. And therefore we readily admit 
that in this department Goethe did all that was possible 
at the time when he lived. I said just now that he 
treated nature like a work of art. In his studies on 
morphology, he reminds one of a spectator at a play, 
with strong artistic sympathies. His delicate instinct 
makes him feel how all the details fall into their places, 
and work harmoniously together, and how some common 
purpose governs the whole ; and yet, while this exquisite 
order and symmetry give him intense pleasure, he cannot 
formulate the dominant idea. That is reserved for the 
scientific critic of the drama, while the artistic spectator 
feels perhaps, as Goethe did in the presence of natural 
phenomena, an antipathy to such dissection, fearing, 
though without reason, that his pleasure may be spoilt 
by it. 

Goethe's point of view in the Theory of Colour is much 
the same. We have seen that he rebels against the 
physical theory just at the point where it gives complete 
and consistent explanations from principles once accepted. 
Evidently it is not the insufficiency of the theory to 
explain individual cases that is a stumbling-block to 
him. He takes offence at the assumption made for the 


sake of explaining the phenomena, which seem to him so 
absurd, that he locks upon the interpretation as no inter- 
pretation at all. Above all, the idea that white light 
could be composed of coloured light seems to have been 
quite inconceivable to him ; at the very beginning of the 
controversy, he rails at the disgusting Newtonian white of 
the natural philosophers, an expression which seems to 
show that this was the assumption that most annoyed him. 
Again, in his later attacks on Newton, which were not 
published till after his Theory of Colour was completed, 
he rather strives to show that Newton's facts might be 
explained on his own hypothesis, and that therefore 
Newton's hypothesis was not fully proved, than attempts 
to prove that hypothesis inconsistent with itself or with 
the facts. Nay, he seems to consider the obviousness of 
his own hypothesis so overwhelming, that it need only be 
brought forward to upset Newton's entirely. There are 
only a few passages where he disputes the experiments 
described by Newton. Some of them, apparently, he could 
not succeed in refuting, because the result is not equally 
easy to observe in all positions of the lenses used, and 
because he was unacquainted with the geometrical rela- 
tions by which the most favourable positions of them are 
determined. In other experiments on the separation of 
simple coloured light by means of prisms alone, Goethe's 
objections are not quite groundless, inasmuch as the isola- 
tion of single colours cannot by this means be so effectu- 
ally carried out, that after refraction through another 
prism there are no traces of other tints at the edges. A 
complete isolation of light of one colour can only be 
effected by very carefully arranged apparatus, consisting 
of combined prisms and lenses, a set of experiments which 
Groethe postponed to a supplement, and finally left un- 
noticed. When he complains of the complication of 
these contrivances, we need only think of the laborious 


and roundabout methods which chemists must often 
adopt to obtain certain elementary bodies in a pure form ; 
and we need not be surprised to find that it is impossible 
to solve a similar problem in the case of light in the 
open air in a garden, and with a single prism in one's 
hand. 1 Goethe must, consistently with his theory, deny 
in toto the possibility of isolating pure light of one colour. 
Whether he ever experimented with the proper apparatus 
to solve the problem remains doubtful, as the supplement 
in which he promised to detail these experiments was 
never published. 

To give some idea of the passionate way in which 
Goethe, usually so temperate and even courtier-like, attacks 
Newton, I quote from a few pages of the controversial 
part of his work the following expressions, which he ap- 
plies to the propositions of this consummate thinker in 
physical and astronomical science ' incredibly impu- 
dent ;' ' mere twaddle ;' ' ludicrous explanation ;' ' admi- 
rable for school-children in a go-cart ;' ' but I see nothing 
will do but lying, and plenty of it.' 2 

Thus, in the theory of colour, Goethe remains faithful 
to his principle, that Nature must reveal her secrets of her 
own free will ; that she is but the transparent representa- 
tion of the ideal world. Accordingly, he demands as a 
preliminary to the investigation of physical phenomena, 
that the observed facts shall be so arranged that one ex- 
plains the other, and that thus we may attain an insight 

1 I venture to add that I am acquainted with the impossibility of decom- 
posing or changing simple coloured light, the two principles which form 
the basis of Newton's theory, not merely by hearsay, but from actual obser- 
vation, having been under the necessity in one of my own researches of 
obtaining light of one colour in a state of the greatest possible purity. (See 
Poggendorft's Annalen, vol. Ixxxvi. p. 50], on Sir D. Brewster's New Analysis 
of Sunlight.} 

2 Something parallel to this extraordinary proceeding of Goethe's may ba 
found in Hobbes's attack on Wallis. TB. 


into their connection without ever having to trust to any 
thing but our senses. This demand of his looks most 
attractive, but is essentially wrong in principle. For a 
natural phenomenon is not considered in physical science 
to be fully explained until you have traced it back to the 
ultimate forces which are concerned in its production and 
its maintenance. Now, as we can never become cognizant 
of forces qua forces, but only of their effects, we are com- 
pelled in eveiy explanation of natural phenomena to 
leave the sphere of sense, and to pass to things which are 
not objects of sense, and are denned only by abstract con- 
ceptions. When we find a stove warm, and then observe 
that a fire is burning in it, we say, though somewhat in- 
accurately, that the former sensation is explained by the 
latter. But in reality this is equivalent to saying, we 
are always accustomed to find heat where fire is burning ; 
now, a fire is burning in the stove, therefore we shall find 
heat there. Accordingly we bring our single fact under 
a more general, better known fact, rest satisfied with it, 
and call it falsely an explanation. Evidently, however, 
the generality of the observation does not necessarily imply 
an insight into causes ; such an insight is only obtained 
when we can make out what forces are at work in the 
fire, and how the effects depend upon them. 

But this step into the region of abstract conceptions, 
which must necessarily be taken, if we wish to penetrate 
to the causes of phenomena, scares the poet away. In 
writing a poem he has been accustomed to look, as it 
were, right into the subject, and to reproduce his intui- 
tion without formulating any of the steps that led him to 
it. And his success is proportionate to the vividness of 
the intuition. Such is the fashion in which he would 
have Nature attacked. But the natural philosopher in- 
sists on transporting him into a world of invisible atoms 
and movements, of attractive and repulsive forces, whose 


intricate actions and reactions, though governed by 
strict laws, can scarcely be taken in at a glance. To 
him the impressions of sense are not an irrefragable 
authority ; he examines what claim they have to be 
trusted ; he asks whether things which they pronounce 
alike are really alike, and whether things which they 
pronounce different are really different ; and often finds 
that he must answer, no ! The result of such examination, 
as at present understood, is that the organs of sense do 
indeed give us information about external effects pro- 
duced on them, but convey those effects to our conscious- 
ness in a totally different form, so that the character of a 
sensuous perception depends not so much on the proper- 
ties of the object perceived as on those of the organ by 
which we receive the information. All that the optic 
nerve conveys to us, it conveys under the form of a sensa- 
tion of light, whether it be the rays of the sun, or a blow 
in the eye, or an electric current passing through it. 
Again, the auditory nerve translates everything into phe- 
nomena of sound, the nerves of the skin into sensations of 
temperature or touch. The same electric current whose 
existence is indicated by the optic nerve as a flash of 
light, or by the organ of taste as an acid flavour, excites 
in the nerves of the skin the sensation of burning. The 
same ray of sunshine, which is called light when it falls 
on the eye, we call heat when it falls on the skin. But 
on the other hand, in spite of their different effects upon 
our organisation, the daylight which enters through our 
windows, and the heat radiated by an iron stove, do not 
in reality differ more or less from each other than the 
red and blue constituents of light. In fact, just as in the 
Undulatory Theory, the red rays are distinguished from 
the blue rays only by their longer period of vibration, 
and their smaller refrangibility, so the dark heat rays of 
the stove have a still longer period and still smaller re- 


frangibility than the red rays of light, but are in every 
other respect exactly similar to them. All these rays, 
whether luminous or non-luminous, have heating proper- 
ties, but only a certain number of them, to which for that 
reason we give the name of light, can penetrate through 
the transparent part of the eye to the optic nerve, and 
excite a sensation of light. Perhaps the relation between 
our senses and the external world may be best enunciated 
as follows : our sensations are for us only symbols of the 
objects of the external world, and correspond to them 
only in some such way as written characters or articulate 
words to the things they denote. They give us, it is true, 
information respecting the properties of things without 
us, but no better information than we give a Wind man 
about colour by verbal descriptions. 

We see that science has arrived at an estimate of the 
senses very different from that which, was present to the 
poet's mind. And Newton's assertion that white was 
composed of all the colours of the spectrum was the first 
germ of the scientific view which has subsequently been 
developed. For at that time there were none of those 
galvanic observations which paved the way to a know- 
ledge of the functions of the nerves in the production of 
sensations. Natural philosophers asserted that white, to 
the eye the simplest and purest of all our sensations of 
colour, was compounded of less pure and complex mate- 
rials. It seems to have flashed upon the poet's mind that 
all his principles were unsettled by the results of this 
assertion, and that is why the hypothesis seems to him so 
unthinkable, so ineffably absurd. "We must look upon 
his theory of colour as a forlorn hope, as a desperate at- 
tempt to rescue from the attacks of science the belief in 
the direct truth of our sensations. And this will account, 
for the enthusiasm with which he strives to elaborate and 
to defend his theory, for the passionate irritability with 


which he attacks his opponent, for the overweening im- 
portance which he attaches to these researches in com- 
parison with his other achievements, and for his inacces- 
sibility to conviction or compromise. 

If we now turn to Groethe's own theories on the subject, 
we must, on the grounds above stated, expect to find that 
he cannot, without being untrue to his own principle, 
give us anything deserving to be called a scientific ex- 
planation of the phenomena, and that is exactly what 
happens. He starts with the proposition that all colours 
are darker than white, that they have something of shade 
in them (on the physical theory, white compounded of all 
colours must necessarily be brighter than any of its 
constituents). The direct mixture of dark and light, of 
black and white, gives grey ; the colours must therefore 
owe their existence to some form of the co-operation of 
light and shade. Groethe imagines he has discovered 
it in the phenomena presented by slightly opaque or 
ha/y media. Such media usually look blue when the 
light falls on them, and they are seen in front of a dark 
object, but yellow when a bright object is looked at 
through them. Thus in the day time the air looks blue 
against the dark background of the sky, and the sun, 
when viewed, as is the case at sunset, through a thick 
and hazy stratum of air, appears yellow. The physical 
explanation of this phenomenon, which, however, is not 
exhibited by all such media, as, for instance, by plates 
of unpolished glass, would lead us too far from the sub- 
ject. According to Groethe, the semi-opaque medium 
imparts to the light something corporeal, something 
of the nature of shade, such as is requisite, he would 
say, for the formation of colour. This conception alone 
is enough to perplex anyone who looks upon it as a 
physical explanation. Does he mean to say that ma- 
terial particles mingle with the light and fly away with 


it ? But this is Groethe's fundamental experiment, this 
is the typical phenomenon under which he tries to reduce 
all the phenomena of colour, especially those connected 
with the prismatic spectrum. He looks upon all trans- 
parent bodies as slightly hazy, and assumes that the 
prism imparts to the image which it shows to an observer 
something of its own opacity. Here, again, it is hard to 
get a definite conception of what is meant. Groethe 
seems to have thought that a prism never gives per- 
fectly defined images, but only indistinct, half-obliterated 
ones, for he puts them all in the same class with the 
double images which are exhibited by parallel plates of 
glass and by Iceland spar. The images formed by a 
prism are, it is true, indistinct in compound light, but 
they are perfectly defined when simple light is used. If 
you examine, he says, a bright surface on a dark ground 
through a prism, the image is displaced and blurred by 
the prism. The anterior edge is pushed forward over the 
dark background, and consequently a hazy light on a 
dark ground appears blue, while the other edge is covered 
by the image of the black surface which comes after it, 
and, consequently, being a light image behind a hazy 
dark colour, appears yellowish-red. But why the an- 
terior edge appears in front of the ground, the posterior 
edge behind it, and not vice versa, he does not explain. 
Let us analyse this explanation, and try to grasp clearly 
the conception of an optical image. When I see a 
bright object reflected in a mirror, the reason is that 
the light which proceeds from it is thrown back exactly 
as if it came from an object of the same kind behind the 
mirror. The eye of the observer receives the impression 
accordingly, and therefore he imagines he really sees the 
object. Everyone knows there is nothing real behind 
the mirror to correspond to the image that no light can 
penetrate thither, but that what is called the image is 


simply a geometrical point, in which the reflected rays, 
if produced backwards, would intersect. And, accordingly, 
no one expects the image to produce any real effect 
behind the mirror. In the same way the prism shows 
us images of objects which occupy a different position 
from the objects themselves ; that is to say, the light 
which an object sends to the prism is refracted by it, so 
that it appears to come from an object lying to one side, 
called the image. This image, again, is not real ; it is, as 
in the case of reflection, the geometrical point in which 
the refracted rays intersect when produced backwards. 
And yet, according to Goethe, this image is to produce 
real effects by its displacement ; the displaced patch of 
light makes, he says, the dark space behind it appear 
blue, just as an imperfectly transparent body would, and 
so again the displaced dark patch makes the bright space 
behind appear reddish-yellow. That Goethe really treats 
the image as an actual object in the place it appears to 
occupy is obvious enough, especially as he is compelled 
to assume, in the course of his explanation, that the 
blue and red edges of the bright space are respectively 
before and behind the dark image which, like it, is 
displaced by the prism. He does, in fact, remain loyal 
to the appearance presented to the senses, and treats a 
geometrical locus as if it were a material object. Again, 
he does not scruple at one time to make red and blue 
destroy each other, as, for example, in the blue edge of a 
red surface seen through the prism, and at another to 
construct out of them a beautiful purple, as when the 
blue and red edges of two neighbouring white surfaces 
meet in a black ground. And when he comes to Newton's 
more complicated experiments, he is driven to still more 
marvellous expedients. As long as you treat his explana- 
tions as a pictorial way of representing the physical 
processes, you may acquiesce in them, and even frequently 


find them vivid and characteristic, but as physical eluci- 
dations of the phenomena they are absolutely irrational. 

In conclusion, it must be obvious to everyone that the 
theoretical part of the Theory of Colour is not natural 
philosophy at all ; at the same time we can, to a certain 
extent, see that the poet wanted to introduce a totally 
different method into the study of Nature, and more or 
less understand how he came to do so. Poetry is con- 
cerned solely with the ' beautiful show ' which makes it 
possible to contemplate the ideal; how that show is 
produced is a matter of indifference. Even Nature is, in 
the poet's eyes, but the sensible expression of the spiritual. 
The natural philosopher, on the other hand, tries to 
discover the levers, the cords, and the pulleys, which 
work behind the scenes, and shift them. Of course the 
sight of the machinery spoils the beautiful show, and 
therefore the poet would gladly talk it out of existence, 
and ignoring cords and pulleys as the chimeras of a 
pedant's brain, he would have us believe that the scenes 
shift themselves, or are governed by the idea of the 
drama. And it is just characteristic of Groethe, that he, 
and he alone among poets, must needs break a lance 
with natural philosophers. Other poets are either so 
entirely carried away by the fire of their enthusiasm that 
they do not trouble themselves about the disturbing 
influences of the outer world, or else they rejoice in the 
triumphs of mind over matter, even on that unpropitious 
battlefield. But Groethe, whom no intensity of subjective 
feeling could blind to the realities around him, cannot 
rest satisfied until he has stamped reality itself with the 
image and superscription of poetry. This constitutes 
the peculiar beauty of his poetry, and at the same time 
fully accounts for his resolute hostility to the machinery 
that every moment threatens to disturb his poetic repose, 
and for his determination to attack the enemy in his own 


But we cannot triumph over the machinery of matter 
by ignoring it ; we can triumph over it only by subordi- 
nating it to the aims of our moral intelligence. We must 
familiarise ourselves with its levers and pulleys, fatal 
though it be to poetic contemplation, in order to be able 
to govern them after our own will, and therein lies the 
complete justification of physical investigation, and its 
vast importance for the advance of human civilisation. 

From what I have said it will be apparent that 
Goethe did follow the same line of thought in all his 
contributions to science, but that the problems he en- 
countered were of diametrically opposite characters. And, 
perhaps, when it is understood how the self-same cha- 
racteristic of his intellect, which in one branch of science 
won for him immortal renown, entailed upon him egre- 
gious failure in the other, it will tend to dissipate, in the 
minds of many worshippers of the great poet, a lingering 
prejudice against natural philosophers, whom they sus- 
pect of being blinded by narrow professional pride to the 
loftiest inspirations of genius. 




LADIES AND G-ENTLEMEN, In the native town of Beet- 
i hoven, the mightiest among the heroes of harmony, no 
subject seemed to me better adapted for a popular 
audience than music itself. Following, therefore, the 
direction of my researches during the last few years, I 
will endeavour to explain to you what physics and physio- 
logy have to say regarding the most cherished art of the 
Rhenish land music and musical relations. Music has 
Litherto withdrawn itself from scientific treatment more 
than any other art. Poetry, painting, and sculpture 
borrow at least the material for their delineations from 
the world of experience. They portray nature and man. 
Not only can their material be critically investigated in 
respect to its correctness and truth to nature, but scien- 
tific art-criticism, however much enthusiasts may have 
disputed its right to do so, has actually succeeded in 
making some progress in investigating the causes of that 
aesthetic pleasure which it is the intention of these arts to 
dte. In music, on the other hand, it seems at first 



sight as if those were still in the right who reject all 
' anatomisation of pleasurable sensations.' This art, bor- 
rowing no part of its material from the experience of our 
senses ; not attempting to describe, and only exceptionally 
to imitate the outer world, necessarily withdraws from 
scientific consideration the chief points of attack which 
other arts present, and hence seems to be as incompre- 
hensible and wonderful as it is certainly powerful in its 
effects. We are, therefore, obliged, and we purpose, to 
confine ourselves, in the first place, to a consideration of 
the material of the art, musical sounds or sensations. It 
always struck me as a wonderful and peculiarly inte- 
resting mystery, that in the theory of musical sounds, in 
the physical and technical foundations of music, which 
above all other arts seems in its action on the mind as 
the most immaterial, evanescent, and tender creator of 
incalculable and indescribable states of consciousness, 
that here in especial the science of purest and strictest 
thought mathematics should prove preeminently fer- 
tile. Thorough bass is a kind of applied mathematics. 
In considering musical intervals, divisions of time, and 
so forth, numerical fractions, and sometimes even loga- 
rithms, play a prominent part. Mathematics and music ! 
the most glaring possible opposites of human thought ! 
and yet connected, mutually sustained ! It is as if they 
would demonstrate the hidden consensus of all the actions 
of our mind, which in the revelations of genius makes us 
forefeel unconscious utterances of a mysteriously active 

When I considered physical acoustics from a physiolo- 
gical point of view, and thus more closely followed up 
the part which the ear plays in the perception of musical 
sounds, much became clear of which the connection had 
not been previously evident. I will attempt to inspire 
you with some of the interest which these questions have 


awakened in my own mind, by endeavouring to exhibit 
a few of the results of physical and physiological 

The short space of time at my disposal obliges me to con- 
fine my attention to one particular point ; but I shall select 
the most important of all, which will best show you the 
significance and results of scientific investigation in this 
field ; I mean the foundation of concord. It is an acknow- 
ledged fact that the numbers of the vibrations of concor- 
dant tones bear to each other ratios expressible by small 
whole numbers. But why ? What have the ratios of 
small whole numbers to do with concord ? This is an old 
riddle, propounded by Pythagoras, and hitherto unsolved. 
Let us see whether the means at the command of modern 
science will furnish the answer. 

First of all, what is a musical tone ? Common expe- 
rience teaches us that all sounding bodies are in a state 
of vibration. This vibration can be seen and felt ; and 
in the case of loud sounds we feel the trembling of the 
air even without touching the sounding bodies. Physical 
science has ascertained that any series of impulses which 
produce a vibration of the air will, if repeated with suffi- 
cient rapidity, generate sound. 

This sound becomes a musical tone, when such rapid 
impulses recur with perfect regularity and in precisely 
equal times. Irregular agitation of the air generates only 
noise. The pitch of a musical tone depends on the 
number of impulses which take place in a given time ; 
the more there are in the same time the higher or sharper 
is the tone. And, as before remarked, there is found to be 
a close relationship between the well-known harmonious 
musical intervals and the number of the vibrations of the 
air. If twice as many vibrations are performed in the 
same time for one tone as for another, the first is the 
octave above the second. If the numbers of vibrations 


in tlie same time are as 2 to 3, the two tones form a fifth ; 
if they are as 4 to 5, the two tones form a major third. 

If you observe that the numbers of the vibrations which 
generate the tones of the major chord C E Gr c are in the 
ratio of the numbers 4:5:6:8, you can deduce from 
these all other relations of musical tones, by imagining 
a new major chord, having the same relations of the num- 
bers of vibrations, to be formed upon each of the above- 
named tones. The numbers of vibrations within the 
limits of audible tones which would be obtained by 
executing the calculation thus indicated, are extraordi- 
narily different. Since the octave above any tone has 
twice as many vibrations as the tone itself, the second 
octave above will have four times, the third has eight 
mes as many. Our modern pianofortes have seven 

taves. Their highest tees, therefore, perform 128 
vibrations in the time that their lowest tone makes one 
single vibration. 

The deepest C l which our pianos usually possess, answers 
to the sixteen-foot open pipe of the organ musicians call 
it the c contra-C ' and makes thirty-three vibrations in 
one second of time. This is very nearly the limit of audi- 
bility. You will have observed that these tones have a 
dull, bad quality of sound on the piano, and that it is 
difficult to determine their pitch and the accuracy of their 
tuning. On the organ the contra-C is somewhat more 
powerful than on the piano, but even here some uncer- 
tainty is felt in judging of its pitch. On larger organs 
there is a whole octave of tones below the contra-C, 
reaching to the next lower C, with 16 J vibrations in a 
second. But the ear can scarcely separate these tones 
from an obscure drone ; and the deeper they are the more 
plainly can it distinguish the separate impulses of the air 
to which they are due. Hence they are used solely in con- 
junction with the next higher octaves, to strengthen their 
notes, arid produce an impression of greater depth. 


With the exception of the organ, all musical instru- 
ments, however diverse the methods in which their sounds 
are produced, have their limit of depth at about the same 
point in the scale as the piano ; not because it would be 
impossible to produce slower impulses of the air of suffi- 
cient power, but because the ear refuses its office, and 
hears slower impulses separately, without gathering them 
up into single tones. 

The often repeated assertion of the French physicist 
Savart, that he heard tones of eight vibrations in a 
second, upon a peculiarly constructed instrument, seems 
due to an error. 

Ascending the scale from the contra-C, pianofortes 
usually have a compass of seven octaves, up to the so- 
called five-accented c, which has 4,224 vibrations in a 
second. Among orchestral instruments it is only the 
piccolo flute which can reach as high, and this will give 
even one tone higher. The violin usually mounts no 
higher than the e below, which has 2,640 vibrations of 
course we except the gymnastics of heaven-scaling virtuosi, 
who are ever striving to excruciate their audience by 
some new impossibility. Such performers may aspire 
to three whole octaves lying above the five-accented c, 
and very painful to the ear, for their existence has been 
established by Despretz, who, by exciting small tuning- 
forks with a violin bow, obtained and heard the eight- 
accented c, having 32,770 vibrations in a second. Here 
the sensation of tone seemed to have reached its upper 
limit, and the intervals were really undistinguishable in 
the later octaves. 

The musical pitch of a tone depends entirely on the 
number of vibrations of the air in a second, and not at 
all upon the mode in which they are produced. It is 
quite, indifferent whether they are generated by the 
vibrating strings of a piano or violin, the vocal chords of 


the human larynx, the metal tongues of the harmonium, 
the reeds of the clarionet, oboe and bassoon, the trembling 
lips of the trumpeter, or the air cut by a sharp edge in 
organ pipes and flutes. 

A tone of the same number of vibrations has always 
th-9 same pitch, by whichever one of these instruments it 
is produced. That which distinguishes the note A of a 
piano for example, from the equally high A of the violin, 
flute, clarionet, or trumpet, is called the quality of the 
tone, and to this we shall have to recur presently. 

As an interesting example of these assertions, I beg to show 
you a peculiar physical instrument for producing musical tones, 
called the siren, Fig. 1, which is especially adapted to establish 
the properties resulting from the ratios of the numbers of vibra- 

In order to produce tones upon this instrument, the portvents 
go and gj are connected by means of flexible tubes with a 
bellows. The air enters into round brass boxes, a and a 1? and 
escapes by the perforated covers of these boxes at c and c^ But 
the holes for the escape of air are not perfectly free. Immediately 
before the covers of both boxes there are two other perforated 
discs, fastened to a perpendicular axis k, which turns with great 
readiness. In the figure, only the perforated disc can be seen at 
c , and immediately below it is the similarly perforated cover of 
the box. In the upper box, Cj, only the edge of the disc is 
visible. If then the holes of the disc are precisely opposite to 
those of the cover, the air can escape freely. But if the disc is 
made to revolve, so that some of its unperforated portions stand 
before the holes of the box, the air cannot escape at all. On 
turning the disc rapidly, the vent-holes of the box are alternately 
opened and closed. During the opening, air escapes; during 
the closure, no air can pass. Hence the continuous stream of 
air from the bellows is converted into a series of discontinuous 
puffs, which, when they follow one another with sufficient 
rapidity, gather themselves together into a tone. 

Each of the revolving discs of this instrument (which is more 
complicated in its construction than any one of the kind hitherto 
made, ancj hence admits of a much greater number of combina- 




tions of tone) has four concentric circles of holes, the lower set 
having 8, 10, 12, 18, and the upper set 9, 12, 15, and 16, holes 
respectively. The series of holes in the covers of the boxes are 
precisely the same as those in the discs, but under each of them 
lies a perforated ring, which can be so arranged, by means of the 
stops i i i i, that the corresponding holes of the cover can either 
communicate freely with the inside of the box, or are entirely 
cut off from it. We are thus enabled to use any one of the 
eight series of holes singly, or combined two and two, or three 
and three together, in any arbitrary manner. 

The round boxes, h h and hj hj, of which halves only are 
drawn in the figure, serve by their resonance to soften the harsh- 
ness of the tone. 

The holes in the boxes and discs are cut obliquely, so that 
when the air enters the boxes through one or more of the series 
of holes, the wind itself drives the discs round with a per- 
petually increasing velocity. 

On beginning to blow the instrument, we first hear separate 
impulses of the air, escaping as puffs, as often as the holes of 
the disc pass in front of those of the box. These puffs of air 
follow one another more and more quickly, as the velocity of 
the revolving discs increases, just like the puffs of steam of a 
locomotive on beginning to move with the train. They next 
produce a whirring and whizzing, which constantly becomes 
more rapid. At last we hear a dull drone, which, as the 
velocity further increases, gradually gains in pitch and strength. 

Suppose that the discs have been brought to a velocity of 
33 revolutions in a second, and that the series with 8 holes has 
been opened. At each revolution of the disc all these 8 holes 
will pass before each separate hole of the cover. Hence there 
will be 8 puffs for each revolution of the disc, or 8 times 33, 
that is, 264 puffs in a second. ThJ gives us the once-accented c' 
of our musical scale, [that is ' middle c,' written on the leger line 
between the bass and treble staves.] But on opening the series 
of 16 holes instead, we have twice as many, or 16 times 33, 
that is, 528 vibrations in a second. We hear exactly the octave 
above the first c', that is the twice-accented c", [or c on the third 
space of the treble staff.] By opening both the series of 8 and 
16 holes at once, we have both c' and c" at once, and can con- 
vince ourselves that we have the absolutely pure concord of the 



octave. By taking 8 and 12 holes, which give numbers of 
vibrations in the ratio of 2 to 3, we have the concord of a 
perfect fifth. Similarly 12 and 16 or 9 and 12 give fourths, 
12 and 15 give a major third, and so on. 

The upper box is furnished with a contrivance for slightly 
sharpening or flattening the tones which it produces. This box 
is movable upon an axis, and connected with a toothed wheel, 
which is worked by the driver attached to the handle d. By 
turning the handle slowly while one of the series of holes in the 
upper box is in use, the tone will be sharper or flatter, according 
as the box moves in the opposite direction to the disc, or in the 
same direction as the disc. When the motion is in the opposite 
direction, the holes meet those of the disc a little sooner than 
they otherwise would, the time of vibration of the tone is 
shortened, and the tone becomes sharper. The contrary ensues 
in the other case. 

Now, on blowing through 8 holes below and 16 above, we 
have a perfect octave, as long as the upper box is still ; but 
when it is in motion, the pitch of the upper tone is slightly 
altered, and the octave becomes false. 

On blowing through 12 holes above and 18 below, the result 
is a perfect fifth as long as the upper box is at rest, but if it 
moves the concord is perceptibly injured. 

These experiments with the siren show us, therefore : 

1. That a series of puffs following one another with sufficient 
rapidity, produce a musical tone. 

2. That the more rapidly they follow one another, the sharper 
is the tone. 

3. That when the ratio of the number of vibrations is exactly 
1 to 2, the result is a perfect octave ; when it is 2 to 3, a 
perfect fifth ; when it is 3 to 4, a pure fourth, and so on. The 
slightest alteration in these ratios destroys the purity of the 

You will perceive, from what has been hitherto ad- 
iuced, that the human ear is affected by vibrations of the 
dr, within certain degrees of rapidity viz. from about 
JO to about 32,000 in a second and that the sensation 
>f musical tone arises from this affection. . 



That the sensation thus excited is a sensation of musical 
tone, does not depend in any way upon the peculiar 
manner in which the air is agitated, but solely on the 
peculiar powers of sensation possessed by our ears and 
auditory nerves. I remarked, a little while ago, that 
when the tones are loud the agitation of the air is per- 
ceptible to the skin. In this way deaf mutes can perceive 
the motion of the air, which we call sound. But they do 
not hear, that is, they have no sensation cf tone in the 
ear. They feel the motion by the nerves of the skin, 
producing that peculiar description of sensation called 
whirring. The limits of the rapidity of vibration within 
which the ear feels an agitation of the air to be sound, 
depend also wholly upon the peculiar constitution of the 

When the siren is turned slowly, and hence the puffs of 
air succeed each other slowly, you hear no musical sound. 
By the continually increasing rapidity of its revolution, 
no essential change is produced in the kind of vibration 
of the air. Nothing new happens externally to the ear. 
The only new result is the sensation experienced by the 
ear, which then for the first time begins to be affected by 
the agitation of the air. Hence the more rapid vibrations 
receive a new name, and are called Sound. If you admire 
paradoxes, you may say that aerial vibrations do not be- 
come sound until they fall upon a hearing ear. 

I must now describe the propagation of sound through 
the atmosphere. The motion of a mass of air through 
which a tone passes, belongs to the so-called wave motions 
a class of motions of great importance in physics. 
Light, as well as sound, is one of these motions. 

The name is derived from the analogy of waves on the 
surface of water, and these will best illustrate the pecu- 
liarity of this description of motion. 

When a point in a surface of still water is agitated as 


by throwing in a stone the motion thus caused is pro- 
pagated in the form of waves, which spread in rings over 
the surface of the water. The circles of waves continue 
to increase even after rest has been restored at the point 
first affected. At the same time the waves become con- 
tinually lower, the further they are. removed from the 
centre of motion, and gradually disappear. On each 
wave-ring we distinguish ridges or crests, and hollows or 

Crest and trough together form a wave, and we measure 
its length from one crest to the next. 

While the wave passes over the surface of the fluid, the 
particles of the water which form it do not move on with 
it. This is easily seen, by floating a chip of straw on the 
water. When the waves reach the chip, they raise or 
depress it, but when they have passed over it, the position 
of the chip is not perceptibly changed. 

Now a light floating chip has no motion different from 
that of the adjacent particles of water. Hence we con- 
clude that these particles do not follow the wave, but, 
after some pitching up and down, remain in their original 
position. That which really advances as a wave is, con- 
sequently, not the particles of water themselves, but only 
a superficial form, which continues to be built up by fresh 
particles of water. The paths of the separate particles of 
water are more nearly vertical circles, in which they re- 
vive with a tolerably uniform velocity, as long as the 
pass over them. 

In Fig. 2 the dark wave-line, ABC, represents a section of 
surface of the water, over which waves are running in the 
direction of the arrows above a and c. The three circles, a, b, 
and c, represent the paths of particular particles of water at the 
surface of the wave. The particle which revolves in the circle b, 
is supposed at the time that the surface of the water presents the 
form A B C, to be at its highest point B, and the particles re- 



volving in the circles a and c to be simultaneously in their lowest 

The respective particles of water revolve in these circles in 
the direction marked by the arrows. The dotted curves repre- 
sent other positions of the passing waves, at equal intervals of 
time, partly before the assumption of the ABC position (as for 
the crests between a and b), and partly after the same (for the 
crests between b and c). The positions of the crests are marked 
with figures. The same figures in the three circles, show where 
the respective revolving particle would be, at the moment the 
wave assumed the corresponding form. It will be noticed that 
the particles advance by equal arcs of the circles, as the crest of 
the wave advances by equal distances parallel to the water level. 

In the circle b it will be further seen, that the particle oi 
water in its positions 1, 2, 3, hastens to meet the approaching 

wave-crests, 1, 2, 3, rises on its left hand side, is then carried on 
by the crest from 4 to 7 in the direction of its advance, after- 
wards halts behind it, sinks down again on the right side, and 
finally reaches its original position at 13. (In the Lecture itself, 
Fig. 2 was replaced by a working model, in which the movable 
particles, connected by threads, really revolved in circles, while 
connecting elastic threads represented the surface of the water.) 

All particles at the surface of the water, as you see by this 
drawing, describe equal circles. The particles of water at dif- 
ferent depths move in the same way, but as the depths increase, 
the diameters of their circles of revolution rapidly diminish. 

In this way, then, arises the appearance of a progressive motion 
along the surface of the water, while in reality the moving par- 
ticles of water do not advance with the wave, but perpetually 
revolve in their small circular orbits. 


To return from waves of water to waves of sound. 
Imagine an elastic fluid like air to replace the water, and 
the waves of this replaced water to be compressed by an 
inflexible plate laid on their surface, the fluid being pre- 
vented from escaping laterally from the pressure. Then 
on the waves being thus flattened out, the ridges where 
the fluid had been heaped up will produce much greater 
density than the hollows, from which tlae fluid had been 
removed to form the ridges. Hence the ridges are re- 
placed by condensed strata of air, and the hollows by 
rarefied strata. Now further imagine that these com- 
pressed waves are propagated by the same law as before, 
and that also the vertical circular orbits of the several 
particles of water are compressed into horizontal straight 
lines. Then the waves of sound will retain the peculiarity 
of having the particles of air only oscillating backwards 
and forwards in a straight line, while the wave itself 
remains merely a progressive form of motion, continually 
composed of fresh particles of air. The immediate result 
then would be waves of sound spreading out horizontally 
from their origin. 

But the expansion of waves of sound is not limited, 
like those of water, to a horizontal surface. They can 
spread out in any direction whatsoever. Suppose the circles 
generated by a stone thrown into the water to extend in 
all directions of space, and you will have the spherical 
waves of air by which sound is propagated. 

Hence we can continue to illustrate the peculiarities of 
the motion of sound, by the well-known visible motions 
of waves of water. 

The length of a wave of water, measured from crest to 
crest, is extremely different. A falling drop, or a breath 
of air, gently curls the surface of the water. The waves 
in the wake of a steamboat toss the swimmer or skiff 
severely. But the waves of a stormy ocean can find room 


in their hollows for the keel of a ship of the line, and 
their ridges can scarcely be overlooked from the mast- 
head. The waves of sound present similar differences. 
The little curls of water with short lengths of wave corre- 
spond to high tones, the giant ocean billows to deep tones. 
Thus the contrabass C has a wave thirty-five feet long, its 
higher octave a wave of half the length, while the highest 
tones of a piano have waves of only three inches in length. 1 
You perceive that the pitch of the tone corresponds 
to the length of the wave. To this we should add that 
the height of the ridges, or, transferred to air, the degree 
of alternate condensation and rarefaction, corresponds to 
the loudness and intensity of the tone. But waves of the 
same height may have different forms. The crest of 
the ridge, for example, may be rounded off or pointed. 
Corresponding varieties also occur in waves of sound of 
the same pitch and loudness. The so-called timbre or 
quality of tone is what corresponds to the form of the 
waves of water. The conception of form is transferred 
from waves of water to waves of sound. Supposing waves 
of water of different forms to be pressed flat as before, the 
surface, having been levelled, will of course display no 
differences of form, but, in the interior of the mass of 
water, we shall have different distributions of pressure, 
and hence of density, which exactly correspond to the 
differences of form in the still uncompressed surface. In 
this sense then we can continue to speak of the form of 
waves of sound, and can represent it geometrically. We 
make the curve rise where the pressure, and hence density, 
increases, and fall where it diminishes just as if we had 

1 The exact lengths of waves corresponding to certain notes, or symbols 
af .tone, depend upon the standard pitch assigned to one particular note, 
and this differs in different countries. Hence the figures of the author 
have been left unreduced. They are sufficiently near to those usually 
adopted in England, to occasion no difficulty to the reader in these general 
remarks. TE. 


a compressed fluid beneath the curve, which would expand 
to the height of the curve in order to regain its natural 

Unfortunately, the form of waves of sound, on which 
depends the quality of the tones produced by various 
sounding bodies, can at present be assigned in only a very 
few cases. 

Among the forms of waves of sound which we are able 
to determine with more exactness, is one of great im- 
portance, here termed the simple or pure wave-form, and 
represented in Fig. 3. 

FIG. 3. 

It can be seen in waves of water only when their height 
is small in comparison with their length, and they run 
over a smooth surface without external disturbance, or 
without any action of wind. Eidge and hollow are gently 
rounded off, equally broad and symmetrical, so that, if we 
inverted the curve, the ridges would exactly fit into the 
hollows, and conversely. This form of wave would be 
more precisely defined by saying that the particles of 
water describe exactly circular orbits of small diameters, 
with exactly uniform velocities. To this simple wave- 
form corresponds a peculiar species of tone, which, from 
reasons to be hereafter assigned, depending upon its rela- 
tion to quality, we will term a simple tone. Such tones 
are produced by striking a tuning-fork, and holding it 
before the opening of a properly-tuned resonance tube. 
The tone of tuneful human voices, singing the vowel oo 
in too, in the middle positions of their register, appears 

()t to differ materially from this form of wave. 
We also know the laws of the motion of strings with 



sufficient accuracy to assign in some cases the form of 
motion which they impart to the air. Thus Fig. 4 repre- 
sents the forms successively assumed by a string struck, 
as in the German Zither, by a pointed style, [the plectrum 

FIG. 4. 

of the ancient lyra, or the quill of the old harpsichord, 
which may be easily imitated on a guitar]. A a represents 
the form assumed by the string at the moment of percus- 
sion. Then, at equal intervals of time, follow the forms 
B, C, D, E, F, Gr ; and then in inverse order, F, E, D, C, 
B, A, and so on in perpetual repetition. The form of 
motion which such a string, by means of an attached sound- 
ing board, imparts to the surrounding air, probably corre- 
sponds to the broken line in Fig. 5, where h h indicates 
the position of equilibrium, and the letters a b c d e f g 
show the line of the wave which is produced by the action 



of several forms of string marked by the corresponding 
capital letters in Fig. 4. It is easily seen how greatly 
this form of wave (which of course could not occur in 

FIG. 5. 

a c e g e 


water) differs from that of Fig. 3 (independently of mag- 
nitude), as the string only imparts to the air a series of 
short impulses, alternately directed to opposite sides. 1 

The waves of air produced by the tone of a violin 
would, on the same principle, be represented by Fig. 6. 

FIG. 6. 


During each period of vibration the pressure increases 
uniformly, and at the end falls back suddenly to its 

It is to such differences in the forms of the waves of 
sound that the variety of quality in musical tones is due. 
We may even carry the analogy further. The more uni- 
formly rounded the form of wave, the softer and milder is 
the quality of tone. The more jerking and angular the 
ave-form, the more piercing the quality. Tuning-forks, 
ith their rounded forms of wave (Fig. 3), have an extra- 
ordinarily soft quality; and the qualities of tone generated 
by the zither and violin resemble in harshness the angu- 
larity of their wave-forms. (Figs. 5 and 6.) 

1 It is here assumed that the sounding-board and air in contact with it 
immediately obey the impulse given by the end of the string without 
exercising a perceptible reaction on the motion of the string. 


Finally, I would direct your attention to an instructive 
spectacle, which I have never been able to view without a 
certain degree of physico-scientific delight, because it dis- 
plays to the bodily eye, on the surface of water, what 
otherwise could only be recognised by the mind's eye of 
the mathematical thinker in a mass of air traversed in all 
directions by waves of sound. I allude to the composition 
of many different systems of waves, as they pass over one 
another, each undisturbedly pursuing its own path. We 
can watch it from the parapet of any bridge spanning a 
river, but it is most complete and sublime when viewed 
from a cliff beside the sea. It is then rare not to see 
innumerable systems of waves, of various length, propa- 
gated in various directions. The longest come from the 
deep sea and dash against the shore. Where the boiling 
breakers burst shorter waves arise, and run back again 
towards the sea. Perhaps a bird of prey darting after a 
fish gives rise to a system of circular waves, which, 
rocking over the undulating surface, are propagated with 
the same regularity as on the mirror of an inland lake. 
And thus, from the distant horizon, where white lines of 
foam on the steel-blue surface betray the coming trains of 
wave, down to the sand beneath our feet, where the im- 
pression of their arcs remains, there is unfolded before our 
eyes a sublime image of immeasurable power and unceasing 
variety, which, as the eye at once recognises its pervading 
order and law, enchains and exalts without confusing the 

Now, just in the same way you must conceive the air 
of a concert-hall or ballroom traversed in every direction, 
and not merely on the surface, by a variegated crowd of 
intersecting wave-systems. From the mouths of the male 
singers proceed waves of six to twelve feet in length ; 
from the lips of the songstresses dart shorter waves, from 
eighteen to thirty-six inches long. The rustling of silken 


skirts excites little curls in the air, each instrument in 
the orchestra emits its peculiar waves, and all these sys- 
tems expand spherically from their respective centres, dart 
through each other, are reflected from the walls of the 
room, and thus rush backwards and forwards, until they 
succumb to the greater force of newly generated tones. 

Although this spectacle is veiled from the material eye, 
we have another bodily organ, the ear, specially adapted to 
. reveal it to us. This analyses the interdigitation of the 
waves, which in such cases would be far more confused 
than the intersection of the water undulations, separates 
the several tones which compose it, and distinguishes the 
voices of men and women nay, even of individuals the 
peculiar qualities of tone given out by each instrument, 
the rustling of the dresses, the footfalls of the walkers, 
and so on. 

It is necessary to examine the circumstances with greater 
minuteness. When a bird of prey dips into the sea, rings 
of waves arise, which are propagated as slowly and regu- 
larly upon the moving surface as upon a surface at rest. 
These rings are cut into the curved surface of the waves 
in precisely the same way as they would have been into 
the still surface of a lake. The form of the external sur- 
face of the water is determined in this, as in other more 
complicated cases, by taking the height of each point to 
be the height of all the ridges of the waves which coin- 
cide at this point at one time, after deducting the sum 
)f all similarly simultaneously coincident hollows. Such 
sum of positive magnitudes (the ridges) and negative 
lagnitudes (the hollows), where the latter have to be 
ibtracted instead of being added, is called an alge- 
)raical sum. Using this term, then, we. may say that 
height of every point of the surface of the water is 
to the algebraical sum of all the portions of the 
;aves which at that moment there concur. 


It is the same with the waves of sound. They, too, are 
added together at every point of the mass of air, as well 
as in contact with the listener's ear. For them also the 
degree of condensation and the velocity of the particles of 
air in the passages of the organ of hearing are equal to the 
algebraical sums of the separate degrees of condensation 
and of the velocities of the waves of sound, considered 
apart. This single motion of the air produced by the 
simultaneous action of various sounding bodies, has now* 
to be analysed by the ear into the separate parts which 
correspond to their separate effects. For doing this the 
ear is much more unfavourably situated than the eye. 
The latter surveys the whole undulating surface at a 
glance. But the ear can, of course, only perceive the 
motion of the particles of air which impinge upon it. 
And yet the ear solves its problem with the greatest 
exactness, certainty, and determinacy. This power of the 
ear is of supreme importance for hearing. Were it not 
present it would be impossible to distinguish different 

Some recent anatomical discoveries appear to give a 
clue to the explanation of this important power of the 

You will all have observed the phenomena of the sym- 
pathetic production of tones in musical instruments, espe- 
cially stringed instruments. The string of a pianoforte 
when the damper is raised begins to vibrate as soon as its 
proper tone is produced in its neighbourhood with suffi- 
cient force by some other means. When this foreign tone 
ceases the tone of the string will be heard to continue 
some little time longer. If we put little paper riders on 
the string they will be jerked off when its tone is thus 
produced in the neighbourhood. This sympathetic action 
of the string depends on the impact of the vibrating 
particles of air against the string and its sounding-board. 


Each separate wave-crest (or condensation) of air which 
passes by the string is, of course, too weak to produce a sen- 
sible motion in it. But when a long series of wave-crests 
(or condensations) strike the string in such a manner that 
each succeeding one increases the slight tremour which 
resulted from the action of its predecessors, the effect 
finally becomes sensible. It is a process of exactly the 
same nature as the swinging of a heavy bell. A powerful 
man can scarcely move it sensibly by a single impulse. A 
boy, by pulling the rope at regular intervals corresponding 
to the time of its oscillations, can gradually bring it into 
violent motion. 

This peculiar reinforcement of vibration depends entirely 
on the rhythmical application of the impulse. When the 
bell has been once made to vibrate as a pendulum in a 
very small arc, and the boy always pulls the rope as it 
falls, and at a time that his pull augments the existing 
velocity of the bell, this velocity, increasing slightly at 
each pull, will gradually become considerable. But if 
the boy apply his power at irregular intervals, sometimes 
increasing and sometimes diminishing the motion of the 
bell, he will produce no sensible effect. 

In the same way that a mere boy is thus enabled to 
swing a heavy bell, the tremours of light and mobile air 
suffice to set in motion the heavy and solid mass of steel 
contained in a tuning-fork, provided that the tone which 
is excited in the air is exactly in unison with that of the 
fork, because in this case also every impact of a wave of 
air against the fork increases the motions excited by the 
like previous blows. 

This experiment is most conveniently performed on a 
fork, Fig. 7, which is fastened to a sounding-board, the 
air being excited by a similar fork of precisely the same 
pitch. If one is struck, the other will be found after a 
few seconds to be sounding also. Then damp the first 



fork, by touching it for a moment with a finger, and the 
second will continue the tone. The second will then 
bring the first into vibration, and so on. 

But if a very small piece of wax be attached to the 
ends of one of the forks, whereby its pitch will be 
rendered scarcely perceptibly lower than the other, the 
sympathetic vibration of the second fork ceases, because 
the times of oscillation are no longer the same in each. 
The blows which the waves of air excited by the first 
inflict upon the sounding board of the second fork, are 
indeed for a time in the same direction as the motions of 

FIG. 7. 

the second fork, and consequently increase the latter, 
but after a very short time they cease to be so, and 
consequently destroy the slight motion which they had 
previously excited. 

Lighter and more mobile elastic bodies, as for example 
strings, can be set in motion by a much smaller number 
of aerial impulses. Hence they can be set in sympathetic 
motion much more easily than tuning forks, and by 
means of a musical tone which is far less accurately in 
unison with themselves, 


Now, then, if several tones are sounded in the neigh- 
bourhood of a pianoforte, no string can be set in sym- 
pathetic vibration unless it is in unison with one of those 
tones. For example, depress the forte pedal (thus raising 
the dampers), and put paper riders on all the strings. 
They will of course leap off when their strings are put in 
vibration. Then let several voices or instruments sound 
tones in the neighbourhood. All those riders, and only 
those, will leap off which are placed upon strings that 
correspond to tones of the same pitch as those sounded. 
You perceive that a pianoforte is also capable of analysing 
the wave confusion of the air into its elementary con- 

The process which actually goes on in our ear is 
probably very like that just described. Deep in the 
petrous bone out of which the internal ear is hollowed, 
lies a peculiar organ, the cochlea or snail shell a cavity 
filled with water, and so called from its resemblance to 
the shell of a common garden snail. This spiral passage 
is divided throughout its length into three sections, 
upper, middle, and lower, by two membranes stretched 
in the middle of its height. The Marchese Corti dis- 
covered some very remarkable formations in the middle 
section. They consist of innumerable plates, micro- 
scopically small, and arranged orderly side by side, like 
the keys of a piano. They are connected at one end with 
the fibres of the auditory nerve, and at the other with 
the stretched membrane. 

Fig. 8 shows this extraordinarily complicated arrange- 
ment for a small part of the partition of the cochlea. The 
arches which leave the membrane at d and are re-inserted 
at e, reaching their greatest height between m and o, 
are probably the parts which are suited for vibration. 
They are spun round with innumerable fibrils, among 
which some nerve fibres can be recognised, coming to 




them through the holes near c. The transverse fibres 
g, h, i, k, and the cells o, also appear to belong to the 
nervous system. There are about three thousand arches 
similar to d e, lying orderly beside each other, like the 
keys of a piano in the whole length of the partition of 
the cochlea. 

FIG. 8. 

In the so-called vestibulum, also, where the nerves 
expand upon little membranous bags swimming in water, 
elastic appendages, similar to stiff hairs, have been lately 
discovered at the ends of the nerves. The anatomical 
arrangement of these appendages leaves scarcely any 


room to doubt that they are set into sympathetic vibra- 
tion by the waves of sound which are conducted through 
the ear. Now if we venture to conjecture it is at 
present only a conjecture, but after careful consideration 
I am led to think it very probable that every such 
appendage is tuned to a certain tone like the strings 
of a piano, then the recent experiment with a piano 
shows you that when (and only when) that tone is 
sounded the corresponding hair-like appendage may vibrate, 
and the corresponding nerve-fibre experience a sensa- 
tion> so that the presence of each single such tone in the 
midst of a whole confusion of tones must be indicated 
by the corresponding sensation. 

Experience then shows us that the ear really possesses 
the power of analysing waves of air into their elementary 

By compound motions of the air, we have hitherto 
meant such as have been caused by the simultaneous 
vibration of several elastic bodies. Now, since the forms 
of the waves of sound of different musical instruments 
are different, there is room to suppose that the kind of 
vibration excited in the passages of the ear by one such 
tone will be exactly the same as the kind of vibration 
which in another case is there excited by two or more 
instruments sounded together. If the ear analyses the 
motion into its elements in the latter case, it cannot well 
avoid doing so in the former, where the tone is due to a 
single source. And this is found to be really the case. 

I have previously mentioned the form of wave with 
gently rounded crests and hollows, and termed it simple or 
pure (p. 75). In reference to this form the French mathe- 
matician Fourier has established a celebrated and impor- 
tant theorem which may be translated from mathematical 
into ordinary language thus : Any form of wave what- 
ever can be compounded of a number of simple waves of 



different lengths. The longest of these simple waves 
has the same length as that of the given form of wave, 
the others have lengths one-half, one-third, one-fourth, &c. 
as great. 

By the different modes of uniting the crests and 
hollows of these simple waves, an endless multiplicity of 
wave-forms may be produced. 

For example, the wave-curves A and B, Fig. 9, represent 
FIG. 9. 

waves of simple tones, B making twice as many vibrations as A in 
a second of time, and being consequently an octave higher in pitch. 
C and D, on the other hand, represent the waves which result 
from the superposition of B on A. The dotted curves in the 
first halves of C and D are repetitions of so much of the figure A. 
In C, the initial point e of the curve B coincides with the initial 
point d of A. Bat in D, the deepest point b 2 of the first hollow 
in B is placed under the initial point of A. The result is two 
different compound- curves, the first C having steeply ascending 



and more gently descending crests, but so related that, by re- 
versing the figure, the elevations would exactly fit into the 
depressions. But in D we have pointed crests and flattened 
hollows, which are, however, symmetrical with respect to right 
and left. 

Other forms are shown in Fig. 10, which are also compounded 
of two simple waves, A and B, of which B makes three times as 
many vibrations in a second as A, and consequently is the 

Fia. 10. 

twelfth higher in pitch. The dotted curves in C and D are, as 
before, repetitions of A. C has flat crests and flat hollows, D 
has pointed crests and pointed hollows. 

These extremely simple examples will suffice to give a con- 
ception of the great multiplicity of forms resulting from this 
method of composition. Supposing that instead of two, several 
simple waves were selected, with heights and initial points 
arbitrarily chosen, an endless variety of changes could be 


effected, and, in point of fact, any given form of wave could be 
reproduced. 1 

When various simple waves concur on the surface of 
water, the compound wave-form has only a momentary 
existence, because the longer waves move faster than the 
shorter, and consequently the two kinds of wave imme- 
diately separate, giving the eye an opportunity of recog- 
nising the presence of several systems of waves. But 
when waves of sound are similarly compounded, they 
never separate again, because long and short waves traverse 
air with the same velocity. Hence the compound wave 
is permanent, and continues its course unchanged, so that 
when it strikes the ear, there is nothing to indicate 
whether it originally left a musical instrument in this 
form, or whether it had been compounded on the way, 
out of two or more undulations. 

Now what doe's the ear do? Does it analyse this 
compound wave? Or does it grasp it as a whole? The 
answer to these questions depends upon the sense in 
which we take them. We must distinguish two different 
points the audible sensation, as it is developed with- 
out any intellectual interference, and the conception, 
which we form in consequence of that sensation. We 
have, as it were, to distinguish between the material ear 
of the body and the spiritual ear of the mind. The 
material ear does precisely what the mathematician 
effects by means of Fourier's theorem, and what the 
pianoforte accomplishes when a confused mass of tones is 
presented to it. It analyses those wave-forms which were 
not originally due to simple undulations, such as those 
furnished by tuning forks, into a sum of simple tones, and 

1 Of course the waves could not overhang, but waves of such a form 
would have no possible analogue in waves of sound [which the reader will 
recollect are not actually in the forms here drawn, but have only condensa- 
tions and rarefactions, conveniently replaced by these forms, p. 73]. 


feels the tone due to each separate simple wave sepa- 
rately, whether the compound wave originally proceeded 
from a source capable of generating it, or became com- 
pounded on the way. 

For example, on striking a string, it will give a tone corre- 
sponding, as we have seen, to a wave-form widely different from 
that of a simple tone. When the ear analyses this wave-form 
into a sum of simple waves, it hears at the same time a series of 
simple tones corresponding to these waves. 

Strings are peculiarly favourable for such an investigation, 
because they are themselves capable of assuming extremely dif- 
ferent forms in the course of their vibration, and these forms 
may also be considered, like those of aerial undulations, as com- 
pounded of simple waves. Fig. 4, p. 76, shows the consecutive 
forms of a string struck by a simple rod. Fig. 11, p. 90, gives a 
number of other forms of vibration of a string, corresponding to 
simple tones. The continuous line shows the extreme displace- 
ment of the string in one direction, and the dotted line in the other. 
A.t a the string produces its fundamental tone, the deepest simple 
tone it can produce, vibrating in its whole length, first on one 
side and then on the other. At b it falls into two vibrating 
sections, separated by a single stationary point /3, called a node 
(knot). The tone is an octave higher, the same as each of the 
two sections would separately produce, and it performs twice as 
many vibrations in a second as the fundamental tone. At c we 
have two nodes, yj and y 2 , and three vibrating sections, each 
vibrating three times as fast as the fundamental tone and hence 
giving its twelfth. At d l there are three nodes, 3 1? 3 2 , c> 3 , and 
four vibrating sections, each vibrating four times as quickly as 
the fundamental tone, and giving the second octave above it. 

In the same way forms of vibration may occur with 5, 6, 7 r 
&c., vibrating sections, each performing respectively, 5, 6, 7, &c. 
times as many vibrations in a second as the fundamental tone, 
and all other vibratiorial forms of the string may be conceived as 
compounded of a sum of such simple vibrational forms. 

The vibrational forms with stationary points or nodes may be 
produced, by gently touching the string at one of these points, 
either with the finger or a rod, and rubbing the string with a 



violin bow, plucking it with the finger, or striking it with a 
pianoforte hammer. The bell-like harmonics or flageolet-tones 
of strings, so much used in violin playing, are thus produced. 

Now suppose that a string has been excited, and after its tone 
has been allowed to continue for a moment, it is touched gently 
at its middle point /3, Fig. 11 b, or 2 , Fig. 11 d. The vibra- 
tional forms a and c, for which this point is in motion, will be 
immediately checked and destroyed; but the vibrational forms 
b and d, for which this point is at rest, will not be disturbed, 
and the tones due to them will continue to be heard. In 

FIG. 11. 

this way we can readily discover whether certain members of 
the series of simple tones are contained in the compound tone of 
a string when excited in any given way, and the ear can be ren- 
dered sensible of their existence. 

When once these simple tones in the sound of a string have 
been thus rendered audible, the ear will readily be able to 
observe them in the untouched string, after a little accurate 

The series of tones which are thus made to combine with a 


given fundamental tone, is perfectly determinate. They are tones 
which perform twice, thrice, four times, &c., as many vibrations 
in a second as the fundamental tone. They are called the upper 
partials, or harmonic overtones, of the fundamental tone. If 
this last be c, the series may be written as follows in musical 
notation, [it being understood that, on account of the tempera- 
ment of a piano, these are not precisely the fundamental tones of 
the corresponding strings on that instrument, and that in par- 
ticular the upper partial, b" b, is necessarily much flatter than the 
fundamental tone of the corresponding note on the piano]. 

c c' d' c" <!' g" b"b c'" d'" e'" 

12 3456789 10 

Not only strings, but almost all kinds of musical in- 
struments, produce waves of sound which are more or less 
different from those of simple tones, and are therefore 
capable of being* compounded out of a greater or less 
number of simple waves. The ear analyses them all by 
means of Fourier's theorem better than the best mathe- 
matician, and on paying sufficient' attention can distin- 
guish the separate simple tones due to the corresponding- 
simple waves. This corresponds precisely to our theory 
of the sympathetic vibration of the organs described by 
Corti. Experiments with the piano, as well as the 
mathematical theory of sympathetic vibrations, show that 
any upper partials which may be present will also produce 
sympathetic vibrations. It follows, therefore, that in the 
cochlea of the ear, every external tone will set in sympa- 
thetic vibration, not merely the little plates with their 
accompanying nerve-fibres, corresponding to its funda- 
mental tone, but also those corresponding to all the upper 
partials, and that consequently the latter must be heard 
as well as the former. 

Hence a simple tone is one excited by a succession of 


simple wave-forms. All other wave-forms, such as those 
produced by the greater number of musical instruments, 
excite sensations of a variety of simple tones. 

Consequently, all the tones of musical instruments 
must in strict language, so far as the sensation of musical 
tone is concerned, be regarded as chords with a pre- 
dominant fundamental tone. 

The whole of this theory of upper partials or harmonic 
overtones will perhaps seem new and singular. Probably 
few or none of those present, however frequently they 
may have heard or performed music, and however fine 
may be their musical ear, have hitherto perceived the 
existence of any such tones, although, according to my 
representations, they must be always and continuously 
present. In fact, a peculiar act of attention is requisite 
in order to hear them, and unless we know how to perform 
this act, the tones remain concealed. As you are aware, 
no perceptions obtained by the senses are merely sensa- 
tions impressed on our nervous systems. A peculiar 
intellectual activity is required to pass from a nervous 
sensation to the conception of an external object, which 
the sensation has aroused. The sensations of our nerves 
of sense are mere symbols indicating certain external 
objects, and it is usually only after considerable practice 
that we acquire the power of drawing correct conclusions 
from our sensations respecting the corresponding objects. 
Now it is a universal law of the perceptions obtained 
through the senses, that we pay only so much attention to 
the sensations actually experienced, as is sufficient for us 
to recognise external objects. In this respect we are very 
onesided and inconsiderate partisans of practical utility ; 
far more so indeed than we suspect. All sensations which 
have no direct reference to external objects, we are accus- 
tomed, as a matter of course, entirely to ignore, and we 
do not become aware of them till we make a scientific 


investigation of the action of the senses, or have our 
attention directed by illness to the phenomena of our own 
bodies. Thus we often find patients, when suffering under 
a slight inflammation of the eyes, become for the first 
time aware of those beads and fibres known as mouches 
volantes swimming about within the vitreous humour of 
the eye, and then they often hypochondriacally imagine 
all sorts of coming evils, because they fancy that these 
appearances are new, whereas they have generally existed 
all their lives. 

Who can easily discover, that there is an absolutely 
blind point, the so-called punctum caecum, within the 
retina of every healthy eye ? How many people know 
that the only objects they see single are those at which 
they are looking, and that all other objects, behind or 
before these, appear double ? I could adduce a long, list 
of similar examples, which have not been brought to 
light till the actions of the senses were scientifically in- 
vestigated, and which remain obstinately concealed, till 
attention has been drawn to them by appropriate means 
often an extremely difficult task to accomplish. 

To this class of phenomena belong the upper partial 
tones. It is not enough for the auditory nerve to have a 
sensation. The intellect must reflect upon it. Hence 
nay former distinction of a material and a spiritual ear. 

We always hear the tone of a string accompanied by a 
certain combination of upper partial tones. A different 
combination of such tones belongs to the tone of a flute, 
or of the human voice, or of a dog's howl. Whether a 
violin or a flute, a man or a dog is close by us is a matter 
of interest for us to know, and our ear takes care to dis- 
tinguish the peculiarities of their tones with accuracy. 
The means by which we can distinguish them, however, 
is a matter of perfect indifference. 

Whether the cry of the dog contains the higher octave 


or the twelfth of the fundamental tone, has no practical 
interest for us, and never occupies our attention. The 
upper partials are consequently thrown into that un- 
analysed mass of peculiarities of a tone which we call its 
quality. Now as the existence of upper partial tones 
depends on the wave form, we see, as I was able to 
state previously (p. 74), that the quality of tone corre- 
sponds to the form of wave. 

The upper partial tones are most easily heard when 
they are not in harmony with the fundamental tone, as 
in the case of bells. The art of the bell-founder consists 
precisely in giving bells such a form that the deeper and 
stronger partial tones shall be in harmony with the 
fundamental tone, as otherwise the bell would be un- 
musical, tinkling like a kettle. But the higher partials 
are always out of harmony, and hence bells are unfitted 
for artistic music. 

On the other hand, it follows, from what has been said, 
that the upper partial tones are all the more difficult to 
hear, the more accustomed we are to the compound tones 
of which they form a part. This is especially the case 
with the human voice, and many skilful observers have 
consequently failed to discover them there. 

The preceding theory was wonderfully corroborated by 
leading to a method by which not only I myself, but 
other persons, were enabled to hear the upper partial 
tones of the human voice. 

No particularly fine musical ear is required for this 
purpose, as was formerly supposed, but only proper means 
for directing the attention of the observer. 

Let a powerful male voice sing the note e b" ^EipE to 
the vowel o in ore, close to a good piano. Then lightly 
touch on the piano the note &' b in the next octave 


above, and listen attentively to the sound of the piano as 
it dies away. If this l>' J7 is a real upper partial in the 
compound tone uttered by the singer, the sound of the 
piano will apparently not die away at all, but the corre- 
sponding upper partial of the voice will be heard as if 
the note of the piano continued. 1 By properly varying 
the experiment, it will be found possible to distinguish 
the vowels from one another by their upper partial tones. 
The investigation is rendered much easier by arming 
the ear with small globes of glass or metal, as in Fig. 12. 

FIG. 12. 

The larger opening a is directed to the source of sound, 
and the smaller funnel-shaped end is applied to the drum 
of the ear. The enclosed mass of air, which is almost 
entirely separated from that without, has its own proper 
tone or key-note, which will be heard, for example, on 
blowing across the edge of the opening a. If then this 
proper tone of the globe is excited in the external air, 
either as a fundamental or upper partial tone, the in- 

1 In repeating this experiment the observer must remember that the e & 
of the piano is not a true twelfth below the i'fe. Hence the singer should 
first bo given b' (2 from the piano, which he will naturally sing as b &, an 
octave lower, and then take a true fifth below it. A skilful singer will 
thus hit the true twelfth and produce the required upper partial b' t. On 
the other hand, if he sings eh from the piano, his upper partial b'\i will 
probably beat with that of the piano. TB. 


eluded mass of air is brought into violent sympathetic 
vibration, and the ear thus connected with it hears the 
corresponding tone with much increased intensity. By 
this means it is extremely easy to determine whether the 
proper tone of the globe is or is not contained in a 
compound tone or mass of tones. 

On examining the vowels of the human voice, it is easy 
to recognise^ with the help of such resonators as have just 
been described, that the upper partial tones of each vowel 
are peculiarly strong in certain parts of the scale : thus 
in ore has its upper partials in the neighbourhood of 
b' b, A in father in the neighbourhood of b" fe (an octave 
higher). The following gives a general view of those 
portions of the scale where the upper partials of the 
vowels, as pronounced in the north of Germany, are par- 
ticularly strong. 

Names of Notes. 
/ o'fe ^b"\L tid" 

:-b" fc 







1 oo 

>nders /' 











f ' 






nea? ly 




1 The corresponding English vowel sounds are probably none of them 
precisely the same as those pronounced by the author. It is necessary to 
note this, for a very slight variation in pronunciation would produce a 
change in the fundamental tone, and consequently a more considerable 
change in the position of the upper partials. The tones given by Bonders, 
which are written below the English equivalents, are cited on the authority 
of Helmholtz's Tonempfindungen, 3rd edition, 1870, p. 171, where Helm- 
holtz says : ' Donders's results differ somewhat from mine, partly because 
his refer to a Dutch, and mine to a North German pronunciation, and partly 
because Bonders, not having had the assistance of tuning forks, could net 
always correctly determine the octave to which the sounds belong.' Ako 
(ib. p. 167) the author remarks that b" h answers only to the deep German 
a (which is the broad Scotch a\ or aw without labialisation), and that if the 
brighter Italian a (English a in father) be used, the resonance rises a third, 
to d'". Br. C. L. Merkel, of Leipzig, in his Physioloc/ie der menschlichcn 


The following easy experiment clearly shows that it is 
indifferent whether the several simple tones contained in 
a compound tone like a vowel uttered by the human voice 
come from one source or several. If the dampers of a 
pianoforte are raised, not only do the sympathetic vibra- 
tions of the strings furnish tones of the same pitch as 
those uttered beside it ; but if we sing A (a in father) to 
any note of the piano, we hear an A quite clearly re- 
turned from the strings ; and if E (a in fare or fate), 
(o in hole or ore), and U (oo in cool), be similarly sung to 
the note, E, 0, and U will also be echoed back. It is 
only necessary to hit the note of the piano with great 
exactness. 1 Now the sound of the vowel is produced 

Sprachc, 1866, p. 109, after citing Helmholtz's experiments as detailed in 
his Tonempfindungen, gives the following as 'the pitches of the vowels 
according to his most recent examination of his own habits of speech, as 
accurately as he is able to note them.' 


oo o o a a eu u a a a ee 

in in in in in in in in in in in 

cool hole ore Scotch father French French fat fare fate feel 

man v v ' 


' Here the note a applies to the timbre obscur of A with low larynx, and 
b to the timbre clair of A with high larynx, and similarly the vowel E may 
pass from d" to d' by narrowing the channel in the mouth. The interme- 
diate vowels 0, A, have also two different timbres and hence their pitch is 
not fixed ; the most frequent are consequently written over one another; 
the lower note is for the obscure, and the higher for the bright timbre. 
But the vowel U seems to be tolerably fixed as ', just as its parents U and 
I are upon d and a", and it has consequently the pitch of the ordinary a' 
tuning fork.' TB. 

1 My own experience shows that if any vowel At any pitch be loudly and 
sharply sung, or called out, beside a piano, of which the dampers have been 
raised, that vowel will be echoed back. There is generally a sensible pause 
before the echo is heard. Before repeating the experiment with a new- 
vowel, whether at the same or a different pitch, damp all the strings and 
then again raise the dampers. The result can easily be made audible to a 
hundred persons at once, and it is extremely interesting and instructive. It 
is peculiarly so, if different vowels be sung to the same pitch, so that they 


solely by the sympathetic vibration of the higher strings, 
which correspond with the upper partial tones of the tone 

In this experiment the tones of numerous strings are 
excited by a tone proceeding from a single source, the 
human voice, which produces a motion of the air, equi- 
valent in form, and therefore in quality, to that of this 
single tone itself. 

We have hitherto spoken only of compositions of waves 
of different lengths. We will now compound waves of 
the same length which are moving in the same direction. 
The result will be entirely different, according as the 
elevations of one coincide with those of the other (in 
which case elevations of double the height and depres- 
sions of double the depth are produced), or the elevations 
of one fall on the depressions of the other. If both 
waves have the same height, so that the elevations of one 
exactly fit into the depressions of the other, both eleva- 
tions and depressions will vanish in the second case, and 
the two waves will mutually destroy each other. Simi- 
larly two waves of sound, as well as two waves of water, 
may mutually destroy each other, when the condensations 
of one coincide with the rarefactions of the other. This 
remarkable phenomenon wherein sound is silenced by a 
precisely similar sound, is called the interference of 

This is easily proved by means of the siren already 
described. On placing the upper box so that the puffs of 
air may proceed simultaneously from the rows of twelve 
holes in each wind chest, their effect is reinforced, and 

have all the same fundamental tone, and the tipper partials only differ in 
intensity. For female voices the pitches ^~^:EP~ o! to c" are favourable 

for all vowels. This is a fundamental experiment for the theory of vowel 
sounds, and should be repeated by all who are interested in speech. Ta. 


we obtain the fundamental tone of the corresponding 
tone of the siren very full and strong. But on arranging 
the boxes so that the upper puffs escape when the lower 
series of holes is covered, and conversely, the fundamental 
tone vanishes, and we only hear a faint sound of the first 
upper partial, which is an octave higher, and which is not 
destroyed by interference under these circumstances. 

Interference leads us to the so-called musical beats, 
If two tones of exactly the same pitch are produced 
simultaneously, and their elevations coincide at first, they 
will never cease to coincide, and if they did not coincide 
at first they never will coincide. 

The two tones will either perpetually reinforce, or per- 
petually destroy each other. But if the two tones have only 
approximatively equal pitches, and their elevations at 
first coincide, so that they mutually reinforce each other, 
the elevations of one will gradually outstrip the elevations 
of the other. Times will come when the elevations of the 
one fall upon the depressions of the other, and then other 
times when the more rapidly advancing elevations of the 
one will have again reached the elevations of the other. 
These alternations become oensible by that alternate 
increase and decrease of loudness, which we call a beat. 
These beats may often be heard when two instruments 
which are not exactly in uuison play a note of the same 
name. When the two or three strings which are struck 
by the same hammer on a piano are out of tune, the beats 
may be distinctly heard. Very slow and regular beats 
often produce a fine effect in sostenuto passages, as in 
sacred part-songs, by pealing through the lofty aisles like 
majestic waves, or by a gentle tremour giving the tone a 
character of enthusiasm and emotion. The greater the 
difference of the pitches, the quicker the beats. As long 
as no more than four to six beats occur in a second, 
the ear readily distinguishes the alternate reinforcements 


of the tone. If the beats are more rapid the tone grates 
on the ear, or, if it is high, becomes cutting. A grating 
tone is one interrupted by rapid breaks, like that of the 
letter B, which is produced by interrupting the tone of 
the voice by a tremour of the tongue or uvula. 1 

When the beats become more rapid, the ear finds a 
continually-increasing difficulty when attempting to hear 
them separately, even though there is a sensible rough- 
ness of the tone. At last they become entirely undis- 
tinguishable, and, like the separate puffs which compose 
a tone, dissolve as it were into a continuous sensation 
of tone. 2 

Hence, while every separate musical tone excites in 
the auditory nerve a uniform sustained sensation, two 
tones of different pitches mutually disturb one another, 
and split up into separable beats, which excite a feeling 
of discontinuity as disagreeable to the ear as similar 
intermittent but rapidly repeated sources of excitement 
are unpleasant to the other organs of sense ; for example, 
flickering and glittering light to the eye, scratching with 
a brush to the skin. This roughness of tone is the es- 
sential character of dissonance. It is most unpleasant to 
the ear when the two tones differ by about a semitone, in 
which case, in the middle portions of the scale, from twenty 
to forty beats ensue in a second. When the difference is 
a whole tone, the roughness is less ; and when it reaches 
a third it usually disappears, at least in the higher parts 
of the scale. The (minor or major) third may in conse- 

1 The trill of the uvula is called the Northumbrian burr, and is not 
known out of Northumberland, in England. In France it is called the 
r grasseye or proven fal, and is the commonest Parisian sound of r. The 
uvula trill is also very common in Germany, but it is quite unknown in 
Italy. Tn. 

2 The transition of beats into a harsh dissonance was displayed by means 
of two organ pipes, of which one was gradually put more and more out of 
tune with the other. 


quence pass as a consonance. Even when the fundimental 
tones have such widely-different pitches that they cannot 
produce audible beats, the upper partial tones may beat 
and make the tone rough. Thus, if two tones form a 
fifth (that is, one makes two vibrations in the same time 
as the other makes three), there is one upper partial in 
both tones which makes six vibrations in the same time. 
Now, if the ratio of the pitches of the fundamental tones 
is exactly as 2 to 3, the two upper partial tones of six 
vibrations are precisely alike, and do not destroy the 
harmony of the fundamental tones. But if this ratio is 
only approximatively as 2 to 3, then these two upper 
partials are not exactly alike, and hence will beat and 
roughen the tone. 

It is very easy to hear the beats of such imperfect 
fifths, because, as our pianos and organs are now tuned, 
all the fifths are impure, although the beats are very 
slow. By properly directed attention, or still better 
with the help of a properly tuned resonator, it is easy to 
hear that it is the particular upper partials here spoken 
of, that are beating together. The beats are necessarily 
weaker than those of the fundamental tones, because the 
beating upper partials are themselves weaker. Although 
we are not usually clearly conscious of these beating 
upper partials, the ear feels their effect as a want of 
uniformity or a roughness in the mass of tone, whereas 
a perfectly pure fifth, the pitches being precisely in the 
ratio of 2 to 3, continues to sound with perfect smooth- 
ness, without any alterations, reinforcements, diminutions, 
or roughnesses of tone. As has already been mentioned, 
the siren proves in the simplest manner that the most 
perfect consonance of the fifth precisely corresponds to 
this ratio between the pitches. We have now learned 
the reason of the roughness experienced when any devia- 
tion from that ratio hag been produced. 


Tn the same way two tones, which have their pitches 
exactly in the ratios of 3 to 4, or 4 to 5, and consequently 
form a perfect fourth or a perfect major third, sound 
much better when sounded together, than two others of 
which the pitches slightly deviate from this exact ratio. 
In this manner, then, any given tone being assumed as 
fundamental, there is a precisely determinate number of 
other degrees of tone which can be sounded at the same 
time with it, without producing any want of uniformity 
or any roughness of tone, or which will at least produce 
less roughness than any slightly greater or smaller inter- 
vals of tone under the same circumstances. 

This is the reason why modern music, which is essen- 
tially based on the harmonious consonance of tones, has 
been compelled to limit its scale to certain determinate 
degrees. But even in ancient music, which allowed only 
one part to be sung at a time, and hence had no harmony 
in the modern sense of the word, it can be shown that 
the upper partial tones contained in all musical tones 
sufficed to determine a preference in favour of pro- 
gressions through certain determinate intervals. When 
, an upper partial tone is common to two successive tones 
in a melody, the ear recognises a certain relationship 
between them, serving as an artistic bond of union. 
Time is, however, too short for me to enlarge on this 
topic, as we should be obliged to go far back into the 
history of music. 

I will but mention that there exists another kind of 
secondary tones, which are only heard when two or more 
loudish tones of different pitch are sounded together, and 
are hence termed combinational. 1 These secondary tones 

1 These are of two kinds, differential and summational, according as their 
pitch is the difference or sum of the pitches of the two generating tones. 
The former are the only combinational tones here spoken of. The dis- 
covery of the latter was entirely due to the theoretical investigations of the 
author. Tit. 


are likewise capable of beating, and hence producing 
roughness in the chords. Suppose a perfectly just major 

_ A 

third c' e r &5Eg:E (ratio of pitches, 4 to 5) is sounded on 
the siren, or with properly-tuned organ pipes, or on a 

violin ; l then a faint C ~r~ two octaves deeper than 
the c' will be heard as a combinational tone. The same 
C is also heard when the tones e f g r m==f= (ratio of 

pitches 5 to 6) are sounded together. 2 

If the three tones cf, e', g', having their pitches precisely 
in the ratios 4, 5, and 6, are struck together, the com- 
binational tone C is produced twice 3 in perfect unison, 
and without beats. But if the three notes are not 
exactly thus tuned, 4 the two C combinational tones will 
have different pitches, and produce faint beats. 

The combinational tones are usually much weaker than 
the upper partial tones, and hence their beats are much 
less rough and sensible than those of the latter. They 
are consequently but little observable, except in tones 
which have scarcely any upper partials, as those produced 
by flutes or the closed pipes of organs. But it is indisput- 
able that on such instruments part-music scarcely presents 
any line of demarcation between harmony and dyshar- 
mony, and is consequently deficient both in strength and 
character. On the contrary, all good musical qualities of 
tone are comparatively rich in upper partials, possessing 

1 In the ordinary tuning of the English concertina this major third is 
just, and generally this instrument shows the differential tones very well. 
The major third is very false on the harmonium and piano. TR. 

2 This minor third is very false on the English concertina, harmonium, or 
piano, and the combinational tone heard is consequently very different 
from the true C. TR. 

3 The combinational tone c, an octave higher, is also produced once 
from the fifth c f g' . TR. 

4 As on the English concertina or harmonium, on both of which the con- 
sequent effect may be well heard. TB. 


the five first, which form the octaves, fifths, and major 
thirds of the fundamental tone. Hence, in the mixture 
stops of the organ, additional pipes are used, giving the 
series of upper partial tones corresponding to the pipe 
producing the fundamental tone, in order to generate a 
penetrating, powerful quality of tone to accompany con- 
gregational singing. The important part played by the 
upper partial tones in all artistic musical effects is here 
also indisputable. 

We have now reached ihe heart of the theory of har- 
mony. Harmony and dysharmony are distinguished by 
the undisturbed current of the tones in the former, 
which are as flowing as when produced separately, and 
by the disturbances created in the latter, in which the 
tones split up into separate beats. All that we have 
considered, tends to this end. In the first place the 
phenomenon of beats depends on the interference of 
waves. Hence they could only occur, if sound were due 
to undulations. Next, the determination of consonant 
intervals necessitated a capability in the ear of feeling 
the upper partial tones, and analysing the compound 
systems of waves into simple undulations, according to 
Fourier's theorem. It is entirely due to this theorem 
that the pitches of the upper partial tones of all service- 
able musical tones must stand to the pitch of their fun- 
damental tones in the ratios of the whole numbers to 1, 
and that consequently the ratios of the pitches of con- 
cordant intervals must correspond with the smallest 
possible whole numbers. How essential is the physio- 
logical constitution of the ear which we have just 
considered, becomes clear by comparing it with that of 
the eye. Light is also an undulation of a peculiar 
medium, the luminous ether, diffused through the uni- 
verse, and light, as well as sound, exhibits phenomena of 
interference. Light, too, has waves of various periodic 


times of vibration, which produce in the eye the sensation 
of colour, red having the greatest periodic time, then 
orange, yellow, green, blue, violet ; the periodic time of 
violet being about half that of the outermost red. But 
the eye is unable to decompose compound systems of 
luminous waves, that is, to distinguish compound colours 
from one another. It experiences from them a single, 
unanalysable, simple sensation, that of a mixed colour. 
It is indifferent to the eye whether this mixed colour 
results from a union of fundamental colours with simple, 
or with non-simple ratios of periodic times. The eye has 
no sense of harmony in the same meaning as the ear. 
There is no music to the eye. 

^Esthetics endeavour to find the principle of artistic 
beauty in its unconscious conformity to law. To-day I 
have endeavoured to lay bare the hidden law, on which de- 
pends the agreeableness" of consonant combinations. It is 
in the truest sense of the word unconsciously obeyed, so 
far as it depends on the upper partial tones, "which, 
though felt by the nerves, are not usually consciously 
present to the mind. Their compatibility or incom- 
patibility however is felt, without the hearer knowing 
the cause of the feeling he experiences. 

These phenomena of agreeableness of tone, as deter- 
mined solely by the senses, are of course merely the first 
step towards the beautiful in music. For the attainment 
of that higher beauty which appeals to the intellect, 
harmony and dysharmony are only means, although essen- 
tial and powerful means. In dysharmony the auditory 
nerve feels hurt by the beats of incompatible tones. Tt 
longs for the pure efflux of the tones into harmony. It 
hastens towards that harmony for satisfaction and rest. 
Thus both harmony and dysharmony alternately urge and 
moderate the flow of tones, while the mind sees in their 
immaterial motion an image of its own perpetually 


streaming thoughts and moods. Just as in the rolling 
ocean, this movement, rhythmically repeated, and yet 
ever varying, rivets our attention and hurries us along. 
But whereas in the sea, blind physical forces alone are at 
work, and hence the final impression on the spectator's 
mind is nothing but solitude in a musical work of art 
the movement follows the outflow of the artist's own 
emotions. Now gently gliding, now gracefully leaping, 
now violently stirred, penetrated or laboriously contend- 
ing with the natural expression of passion, the stream of 
sound, in primitive vivacity, bears over into the hearer's 
soul unimagined moods which the artist has overheard 
from his own, and finally raises him up to that repose of 
everlasting beauty, of which Grod has allowed but few of 
his elect favourites to be the heralds. 

But I have reached the confines of physical science* 
and must close. 




THE world of ice and of eternal snow, as unfolded to us 
on the summits of the neighbouring Alpine chain, so 
stern, so solitary, so dangerous, it may be, has yet its own 
peculiar charm. Not only does it enchain the attention of 
the natural philosopher, who finds in it the most wonderful 
disclosures as to the present and past history of the globe, 
but every summer it entices thousands of travellers of all 
conditions, who find there mental and bodily recreation. 
While some content themselves with admiring from afar 
the dazzling adornment which the pure, luminous masses 
of snowy peaks, interposed between the deeper blue of 
the sky and the succulent green of the meadows, lend to 
the landscape, others more boldly penetrate into the 
strange world, willingly subjecting themselves to the 
most extreme degrees of exertion and danger, if only 
they may fill themselves with the aspect of its sublimity. 

I will not attempt what has so often been attempted in 
vain to depict in words the beauty and magnificence of 
nature, whose aspect delights the Alpine traveller. I 
may well presume that it is known to most of you from 
your own observation ; or, it is to be hoped, will be 
so. But I imagine that the delight and interest in the 


magnificence of those scenes will make you the more 
inclined to lend a willing ear to the remarkable results of 
modern investigations on the more prominent phenomenci 
of the glacial world. There we see that minute pecu- 
liarities of ice, the mere mention of which might at other 
times be regarded as a scientific subtlety, are the causes of 
the most important changes in glaciers ; shapeless masses 
of rock begin to relate their histories to the attentive ob- 
server, histories which often stretch far beyond the past of 
the human race into the obscurity of the primeval world ; 
a peaceful, uniform, and beneficent sway of enormous 
natural forces, where at first sight only desert wastes are 
seen, either extended indefinitely in cheerless, desolate 
solitudes, or full of wild, threatening confusion an arena 
of destructive forces. And thus I think I may promise 
that the study of the connection of those phenomena of 
which I can now only give you a very short outline will 
not only afford you some prosaic instruction, but will 
make your pleasure in the magnificent scenes of the high 
mountains more vivid, your interest deeper, and your 
admiration more exalted. 

Let me first of all recall to your remembrance the chief 
features of the external appearance of the snow-fields and 
of the glaciers ; and let me mention the accurate 
measurements which have contributed to supplement ob- 
servation, before I pass to discuss the causal connection of 
those processes. 

The higher we ascend the mountains the colder it becomes. 
Our atmosphere is like a warm covering spread over the 
earth ; it is well-nigh entirely transparent for the lumi- 
nous darting rays of the sun, and allows them to pass almost 
without appreciable change. But it is not equally pene- 
trable by obscure heat-rays, which, proceeding from heated 
terrestrial bodies, struggle to diffuse themselves into space. 
These are absorbed by atmospheric air, especially when it 


is moist ; the mass of air is itself heated thereby, and 
only radiates slowly into space the heat which has been 
gained. The expenditure of heat is thus retarded as com- 
pared with the supply, and a certain store of heat is 
retained along the whole surface of the earth. But on 
high mountains the protective coating of the atmosphere 
is far thinner the radiated heat of the ground can escape 
thence more freely into space ; there, accordingly, the 
accumulated store of heat and the temperature are far 
smaller than at lower levels. 

To this must be added another property of air which 
acts in the same direction. In a mass of air which ex- 
pands, part of its store of heat disappears ; it becomes 
cooler, if it cannot acquire fresh heat from without. 
Conversely, by renewed compression of the air, the same 
quantity of heat is reproduced which had disappeared du- 
ring expansion. Thus if, for instance, south winds drive 
the warm air of the Mediterranean towards the north, and 
compel it to ascend along the great mountain-wall of the 
Alps, where the air, in consequence of the diminished 
pressure, expands by about half its volume, it thereby 
becomes very greatly cooled for a mean height of 11,000 
feet, by from 18 to 30 C., according as it is moist or dry 
and it thereby deposits the greater part of its moisture as 
rain or snow. If the same wind, passing over to the north 
side of the mountains as Fohn-wind, reaches the valleys 
and plains, it again becomes condensed, and is again 
heated. Thus the same current of air Vhich is warm in 
the plains, both on this side of the chain and on the other, 
is bitterly cold on the heights, and can there deposit snow, 
while in the plain we find it insupportably hot. 

The lower temperature at greater heights, which is due 
to both these causes, is, as we know, very marked on the 
lower mountain chains of our neighbourhood. In central 
Europe it amounts to about 1 C. for an ascent of 480 feet; 


in winter it is less 1 for about 720 feet of ascent. 
In the Alps the differences of temperature at great heights 
are accordingly far more considerable, so that upon the 
higher parts of their peaks and slopes the snow which has 
fallen in winter no longer melts in summer. This line, 
above which snow covers the ground throughout the entire 
year, is well known as the snow-line; on the northern 
side of the Alps it is about 8,000 feet high, on the 
southern side about 8,800 feet. Above the snow-line it 
may on sunny days be very warm ; the unrestrained radi- 
ation of the sun, increased by the light reflected from the 
snow, often becomes utterly unbearable ; so that the 
tourist of sedentary habits, apart from the dazzling of his 
eyes, which he must protect by dark spectacles or by a 
veil, usually gets severely sunburnt in the face and hands, 
the result of which is an inflammatory swelling of the 
skin and great blisters on the surface. More pleasant 
testimonies to the power of the sunshine are the vivid 
colours and the powerful odour of the small Alpine flowers 
which bloom in the sheltered rocky clefts among the snow- 
fields. Notwithstanding the powerful radiation of the sun 
the temperature of the air above the snow-fields only rises 
to 5, or at most 8 ; this, however, is sufficient to melt a 
tolerable amount of the superficial layers of snow. But 
the warm hours and days are too short to overpower the 
great masses of snow which have fallen during colder 
times. Hence the height of the snow-line does not de- 
pend merely on the temperature of the mountain slope, 
but also essentially on the amount of the yearly snow-fall. 
It is lower, for instance, on the moist and warm south 
slope of the Himalayas, than on the far colder but also far 
drier north slope of the same mountain. Corresponding 
to the moist climate of western Europe, the snow-fall 
upon the Alps is very great, and hence the number and 
extent of their glaciers are comparatively considerable, so 


that few mountains of the earth can be compared with 
them in this respect. Such a development of the glacial 
world is, as far as we know, met with only on the Hima- 
layas, favoured by the greater height ; in Greenland and 
in Northern Norway, owing to the colder climate ; in a 
few islands in Iceland ; and in New Zealand, from the 
more abundant moisture. 

Places above the snow-line are thus characterised by 
the fact that the snow which in the course of the year 
falls on its surface, does not quite melt away in summer, 
but remains to some extent. This snow, which one 
summer has left, is protected from the further action 
of the sun's heat by the fresh quantities that fall upon 
it during the next autumn, winter, and spring. Of this 
new snow also next summer leaves some remains, and 
thus year by year fresh layers of snow are accumulated one 
above the other. In those places where such an accu- 
mulation of snow ends in a steep precipice, and its inner 
structure is thereby exposed, the regularly stratified yearly 
layers are easily recognised. 

But it is clear that this accumulation of layer upon 
layer cannot go on indefinitely, for otherwise the height 
of the snow peak would continually increase year by year. 
But the more the snow is accumulated the steeper are the 
slopes, and the greater the weight which presses upon the 
lower and older layers and tries to displace them. Ulti- 
mately a state must be reached in which the snow slopes 
are too steep to allow fresh snow to rest upon them, and 
in which the burden which presses the lower layers down- 
wards is so great that these can no longer retain their 
position on the sides of the mountain. Thus, part of the 
snow which had originally fallen on the higher regions of 
the mountain above the snow-line, and had there been 
protected from melting, is compelled to leave its original 
dtion and seek a new one, which it of course finds only 


below the snow-line on the lower slopes of the mountain, 
and especially in the valleys, where however being exposed 
to the influence of a warmer air, it ultimately melts and 
flows away as water. The descent of masses of snow from 
their original positions sometimes happens suddenly in 
avalanches, but it is usually very gradual in the form of 

Thus we must discriminate between two distinct parts of 
the ice-fields ; that is, first, the snow which originally fell 
called firn in Switzerland above the snow-line, cover- 
ing the slopes of the peaks as far as it can hang on to 
them, and filling up the upper wide kettle-shaped ends 
of the valleys forming widely extended fields of snow or 
firnmeere. Secondly, the glaciers, called in the Tyrol 
firner^ which as prolongations of the snow-fields often 
extend to a distance of from 4,000 to 5,000 feet below 
the snow-line, and in which the loose snow of the 
snow-fields is again found changed into transparent solid 
ice. Hence the name glacier, which is derived from the 
Latin, glades ; French, glace, glacier. 

The outward appearance of glaciers is very character- 
istically described by comparing them with Goethe to 
currents of ice. They generally stretch from the snow- 
fields along the depth of the valleys, filling them through- 
out their entire breadth, and often to a considerable 
height. They thus follow all the curvatures, windings, 
Contractions, and enlargements of the valley. Two glaciers 
frequently meet, the valleys of which unite. The two 
glacial currents then join in one common principal cur- 
rent, filling up the valley common to them both. In 
some places these ice-currents present a tolerably level and 
coherent surface, but they are usually traversed by cre- 
vasses, and both over the surface and through the crevasses 
countless small and large water rills ripple, which carry 
off the water formed by the melting of the ice. United, 
and forming a stream, they burst, through a vaulted arid 



clear blue gateway of ice, out at the lower end of the 
larger glacier. 

On the surface of the ice there is a large quantity of 
blocks of stone, and of rocky debris, which at the lower 
end of the glacier are heaped up and form immense walls ; 
these are called the lateral and terminal moraine of the 
glacier. Other heaps of rock, the central moraine, stretch 
a'ong the surface of the glacier in the direction of its 

FIG. 13. 

length, forming long regular dark lines. These always 
start from the places where two glacier streams coincide 
and unite. The central moraines are in such places to be 
regarded as the continuations of the united lateral 
moraines of the two glaciers. 

The formation of the central moraine is well represented 
in the view above given of the Unteraar Glacier. Fig. 1 3. 


In the background are seen the two glacier currents 
emerging from different valleys ; on the right from the 
Schreckhorn, and on the left from the Finsteraarhorn. 
From the place where they unite the rocky wall occupy- 
ing the middle of the picture descends, constituting the 
central moraine. On the left are seen individual large 
masses of rock resting on pillars of ice, which are known 
as glacier tables. 

To exemplify these circumstances still further, I lay 
before you in Fig- 14 a map of the Mer de Glace of 
Chamouni, copied from that of Forbes. 

The Mer de Glace in size is well known as the largest 
glacier in Switzerland, although in length it is exceeded by 
the Aletsch Glacier. It is formed from the snow-fields that 
cover the heights directly north of Mont Blanc, several of 
which, as the Grande Jorasse, the Aiguille Verte (a, 
Figs. 14 and 15), the Aiguille du Geant (b), Aiguille du 
Midi (c), and the Aiguille du Dm (d), are only 2,000 to 
3,000 feet below that king of the European mountains. 
The snow-fields which lie on the slopes and in the basins 
between these mountains collect in three principal cur- 
rents, the Glacier du Geant, Glacier de Lechaud, and 
Glacier du Talefre, which, ultimately united as represented 
in the map, form the Mer de Glace ; this stretches as an 
ice current 2,600 to 3,000 feet in breadth down into the 
valley of Chamouni, where a powerful stream, the Arvey- 
ron, bursts from its lower end at k, and plunges into the 
Arve. The lowest precipice of the Mer de Glace, which 
is visible from the valley of Chamouni, and forms a large 
cascade of ice, is commonly called Glacier des Bois, from 
a small village which lies below. 

Most of the visitors at Chamouni only set foot on the 
lowest part of the Mer de Glace from the inn at the 
Montanvert, and when they are free from giddiness cross 
the glacier at this place to the little house on the oppo- 



site side, the Chapeau (n). Although, as the map shows, 
only a comparatively very small portion of the glacier is 
thus seen and crossed, this way shows sufficiently the 

FIG. 14. 

magnificent scenes, and also the difficulties of a glacier 
excursion. Bolder wanderers march upwards along the 
glacier to the Jardin, a rocky cliff clothed with some 


vegetation, which divides the glacial current of the Gla- 
cier du Talefre into two branches ; and bolder still they 
ascend yet higher, to the Col du Geant (11,000 feet above 
the sea), and down the Italian side to the valley of Aosta. 

The surface of the Mer de Glace shows four of the 
rocky walls which we have designated as medial moraines. 
The first, nearest the east side of the glacier, is formed 
where the two arms of the Glacier du Talefre unite at the 
lower end of the Jardin ; the second proceeds from the 
union of the glacier in question with the Glacier de 
Lechaud ; the third, from the union of the last with the 
Glacier du Geant ; and the fourth, finally, from the top of 
the rock ledge which stretches from the Aiguille du 
Geant towards the cascade (g) of the Glacier du Geant. 

To give you an idea of the slope and the fall of the 
glacier, I have given in Fig. 15 a longitudinal section of 
it according to the levels and measurements taken by 
Forbes, with the view of the right bank of the glacier. 
The letters stand for the same objects as in Fig. 14 ; p is 
the Aiguille de Lechaud, q the Aiguille Noire, r the 
Mont Tacul, f is the Col du Geant, the lowest point in 
the high wall of rock that surrounds the upper end of 
the snow-fields which feed the Mer de Glace. The base 
line corresponds to a length of a little more than nine 
miles : on the right the heights above the sea are given in 
feet. The drawing shows very distinctly how small in 
most places is the fall of the glacier. Only an approxi- 
mate estimate could be made of the depth, for hitherto 
nothing certain has been made out in reference to it. But 
that it is very deep is obvious from the following indivi- 
dual and accidental observations. 

At the end of a vertical rock wall of the Tacul, the 
edge of the Glacier du Geant is pushed forth, forming an 
ice wall 140 feet in height. This would give the depth 
of one of the upper arms of the glacier at the edge. In 



the middle and after the union 
of the three glaciers the depth 
must be far greater. Somewhat 
below the junction Tyndall and 
Hirst sounded a moulin, that is 
a cavity through which the sur- 
face glacier waters escape, to a 
depth of 1 60 feet ; the guides 
alleged that they had sounded 
a similar aperture to a depth 
of 350 feet, and had found no 
bottom. From the usually deep 
trough shaped or gorge-like form 
of the bottom of the valleys, 
which is constructed solely of 
rock walls, it seems improbable 
that for a breadth of 3,000 feet 
the mean depth should only be 
350 feet ; moreover, from the 
manner in which ice moves, there 
must necessarily be a very thick 
coherent mass beneath the cre- 
vassed part. 

To render these magnitudes 
more intelligible by reference to 
more familiar objects, imagine 
the valley of Heidelberg filled 
with ice up to the Molkencur, 
or higher, so that the whole 
town, with all its steeples and 
the castle, is buried deeply 
beneath it ; if, further, you ima- 
gine this mass of ice, gradually 
extending in height, continued 
from the mouth of the valley up 
to Neckargemiind, that would 
about correspond to the lower 

FIG. 15. 


united ice current of the Mer de Glace. Or, instead 
of the Rhine and the Nahe at Bingen, suppose two ice 
currents uniting which fill the Rhine valley to its upper 
border as far as we can see from the river, and then the 
united currents stretching downwards to beyond Asmann- 
shausen and Burg Rheinstein ; such a current would also 
about correspond to the size of the Mer de Glace. 

Fig. 16, which is a view of the magnificent Gorner 

FIG. 16. 

U lacier seen from below, also gives an idea of the size of 
the masses of ice of the larger glaciers. 

The surface of most glaciers is dirty, from the numerous 
pebbles and sand which lie upon it, and which are heaped 
together the more the ice .under them and among them 
melts away. The ice of the surface has been partially 
destroyed and rendered crumbly. In the depths of the 
crevasses ice is seen of a purity and clearness with which 


nothing that we are acquainted with on the plains can be 
compared. From its purity it shows a splendid blue, 
like that of the sky, only with a greenish hue. Crevasses in 
which pure ice is visible in the interior occur of all sizes ; 
in the beginning they form slight cracks in which a knife 
can scarcely be inserted ; becoming gradually enlarged to 
chasms, hundreds, or even thousands, of feet in length, 
and twenty, fifty, and as much as a hundred feet in 
breadth, while some of them are immeasurably deep. 
Their vertical dark blue walls of crystal ice, glistening 
with moisture from the trickling water, form one of the 
most splendid spectacles which nature can present to us ; 
but, at the same time, a spectacle strongly impregnated 
with the excitement of danger, and only enjoyable by the 
traveller who feels perfectly free from the slightest ten- 
dency to giddiness. The tourist must know how, with 
the aid of well-nailed shoes and a pointed Alpenstock, to 
stand even on slippery ice, and at the edge of a vertical 
precipice the foot of which is lost in the darkness of 
night, and at an unknown depth. Such crevasses cannot 
always be evaded in crossing the glacier; at the lower 
part of the Mer de Glace, for instance, where it is usually 
crossed by travellers, we are compelled to travel along 
some extent of precipitous banks of ice, which are oc- 
casionally only four to six feet in breadth, and on 
each side of which is such a blue abyss. Many a 
traveller, who has crept along the steep rocky slopes 
without fear, there feels his heart sink, and cannot turn 
his eyes from the yawning chasm, for he must first care- 
fully select every step for his feet. And yet these blue 
chasms, which lie open and exposed in the daylight, are 
by no means the worst dangers of the glacier ; though 
indeed we are so organised that a danger which we per- 
ceive, and which therefore we can safely avoid, frightens us 
far more than one which we know to exist, but which 


is veiled from our eyes. So also it is with glacier 
chasms. In the lower part of the glacier they yawn 
before us, threatening death and destruction, and lead us, 
timidly collecting all our presence of mind, to shrink from 
them ; thus accidents seldom occur. On the upper part 
of the glacier, on the contrary, the surface is covered with 
snow ; this, when it falls thickly, soon arches over the 
narrower crevasses of a breadth of from four to eight feet, 
and forms bridges which quite conceal the crevasse, so that 
the traveller only sees a beautiful plane snow surface 
before him. If the snow bridges are thick enough, they 
will support a man ; but they are not always so, and these 
are the places where .men, and even chamois, are so often 
lost. These dangers may readily be guarded against if 
two or three men are roped together at intervals of ten 
or twelve feet. If then one of them falls into a crevasse, 
the two others can hold him, and draw him out again. 

In some places the crevasses may be entered, especially 
at the lower end of a glacier. In the well-known glaciers 
of Grrindelwald, Eosenlaui, and other places, this is facili- 
tated by cutting steps and arranging wooden planks. 
Then anyone who does not fear the perpetually trickling 
water may explore these crevasses, and admire the won- 
derfully transparent and pure crystal walls of these 
caverns. The beautiful blue colour which they exhibit 
is the natural colour of perfectly pure water ; liquid 
water as well as ice is blue, though to an extremely small 
extent, so that the colour is only visible in layers of from 
ten to twelve feet in thickness. The water of the Lake of 
Greneva and of theLago di Garda exhibits the same splendid 
colour as ice. 

The glaciers are not everywhere crevassed ; in places 
where the ice meets with an obstacle, and in the middle 
of great glacier currents the motion of which is uniform, 
the surface is perfectly coherent. 


Fig. 17 represents one of the more level parts of the 
Mer de Glace at the Montanvert, the little house of 
which is seen in the background. The Gries Glacier, 
where it forms the height of the pass from the Upper 
Ehone valley to the Tosa valley, may even be crossed on 

FIG. 17. 

horseback. We find the greatest disturbance of the 
surface of the glacier in those places where it passes 
from a slightly inclined part of its bed to one where the 
slope is steeper. The ice is there torn in all directions 
into a quantity of detached blocks, which by melting 


are usually changed into wonderfully shaped sharp ridges 
and pyramids, and from time to time fall into the inter- 
jacent crevasses with a loud rumbling noise. Seen from a 
distance such a place appears like a wild frozen waterfall, 
and is therefore called a cascade ; such a cascade is seen in 
the Grlacier du Talefre at 1, another is seen in the Grlacier 
du Greant at g, Fig. 14, while a third forms the lower end 
of the Mer de Glace. The latter, already mentioned as 
the Grlacier des Bois, which rises directly from the trough 
of the valley at Chamouni to a height of 1,700 feet, the 
height of the Konigstuhl at Heidelberg, affords at all 
times a chief object of admiration to the Chamouni tourist. 
Fig. 18 represents a view of its fantastically rent blocks 
of ice. 

We have hitherto compared the glacier with a current 
as regards its outer form and appearance. This similarity, 
however, is not rnerely an external one : the ice of the 
glacier does, indeed, move forwards like the water of a 
stream, only more slowly. That this must be the caso 
follows from the considerations by which I have en- 
deavoured to explain the origin of a glacier. For as the 
ice is being constantly diminished at the lower end by 
melting, it would entirely disappear if fresh ice did not 
continually press forward from above, which, again, is 
made up by the snowfalls on the mountain tops. 

But by careful ocular observation we may convince 
ourselves that the glacier does actually move. For the 
inhabitants of the valleys, who have the glaciers constantly 
before their eyes, often cross them, and in so doing make 
use of the larger blocks of stone as sign posts detect 
this motion by the fact that their guide posts gradually 
descend in the course of each year. And as the yearly 
displacement of the lower half of the Mer de Grlace at 
Chamouni amounts to no less than from 400 to 600 feet, 
you can readily conceive that such displacements must 



ultimately be observed, notwithstanding the slow rate at 
which they take place, and in spite of the chaotic confu- 
sion of crevasses and rocks which the glacier exhibits. 

Besides rocks and stones, other objects which have 
accidentally alighted upon the glacier are dragged along. 

FIG. 18. 

In 1788 the celebrated Genevese Saussure, together with 
his son and a company of guides and porters, spent 
sixteen days on the Col du Geant. On descending the rocks 
at the side of the cascade of the Glacier du Geant, they 



left behind them a wooden ladder. This was at the 
foot of the Aiguille Noire, where the fourth band of the Mer 
de Grlace begins ; this line thus marks at the same time 
the direction in which ice travels from this point. In the 
year 1832, that is, forty-four years after, fragments of 
this ladder were found by Forbes and other travellers 
not far below the junction of the three glaciers of the 
Mer de Grlace, in the same line (at s, Fig. 19), from 

FIG. 19. 

which it results that these parts of the glacier must 
on the average have each year descended 375 feet. 

In the year 1827 Hugi had built a hut on the central 
moraine of the Unteraar Glacier for the purpose of 
making observations ; the exact position of this hut was 


determined by himself and afterwards by Agassiz, and 
they found that each year it had moved downwards. 
Fourteen years later, in the year 1841, it was 4,884 feet 
lower, so that every year it had on the average moved 
through 349 feet. Agassiz afterwards found that his 
own hut, which he had erected on the same glacier, had 
moved to a somewhat smaller extent. For these observa- 
tions a long time was necessary. But if the motion 
of the glacier be observed by means of accurate measuring 
instruments, such as theodolites, it is not necessary to 
wait for years to observe that ice moves a single day 
is sufficient. 

Such observations have in recent times been made 
by several observers, especially by Forbes and by Tyn- 
dall. They show that in summer the middle of the 
Mer de Glace moves through twenty inches a day, while 
towards the lower terminal cascade the motion amounts 
to as much as thirty-five inches in a day. In winter the 
velocity is only about half as great. At the edges and 
in the lower layers of the glacier, as in a flow of water, 
it is considerably smaller than in the centre of the sur- 

The upper sources of the Mer de Glace also have 
a slower motion, the Glacier du Geant thirteen inches 
a day, and the Glacier du Lechaud nine inches and a 
half. In different glaciers the velocity is in general 
very various, according to the size, the inclination, the 
amount of snow-fall, and other circumstances. 

Such an enormous mass of ice thus gradually and 
gently moves on, imperceptibly to the casual observer, 
about an inch an hour the ice of the Col du Geant 
will take 120 years before it reaches the lower end 
of the Mer de Glace but it moves forward with un- 
controllable force, before which any obstacles that man 
could oppose to it yield like straws, and the traces 


of which are distinctly seen even on the granite walls 
of the valley. If, after a series of wet seasons, and 
an abundant fall of snow on the heights, the base of 
a glacier advances, not merely does it crush dwelling 
houses, and break the trunks of powerful trees, but the 
glacier pushes before it the boulder walls which form 
its terminal moraine without seeming to experience any 
resistance. A truly magnificent spectacle is this motion, 
so gentle, and so continuous, and yet so powerful and so 

I will mention here that from the way in which the 
glacier moves we can easily infer in what places and 
in what directions crevasses will be formed. For as 
all layers of the glacier do not advance with equal 
velocity, some points remain behind others : for instance, 
the edges as compared with the middle. Thus if we 
observe the distance from a given point at the edge 
to a given point of the middle, both of which were 
originally in the same line, but the latter of which 
afterwards descended more rapidly, we shall find that 
this distance continually increases ; and since the ice 
cannot expand to an extent corresponding to the in- 
creasing distance, it breaks up and forms crevasses, 
as seen along the edge of the glacier in Fig, 20, which 
represents the Grorner Glacier at Zermatt. It would 
lead me too far if I were here to attempt to give a 
detailed explanation of the formation of the more regular 
system of crevasses, as they occur in certain parts of all 
glaciers ; it may be sufficient to mention that the con- 
clusions deducible from the considerations above stated 
are fully borne out by observation. 

I will only draw attention to one point what extremely 
small displacements are sufficient to cause ice to form 
hundreds of crevasses. The section of the Mer de Grlace 
(Fig. 21 9 at g, c, h) shows places where a scarcely 



perceptible change in the inclination of the surface of 
the ice occurs of from two to four degrees. This is 
sufficient to produce a system of cross crevasses on the 
surface. Tyndall more especially has urged and con- 
6rmed by observation and measurements, that the mass 
of ice of the glacier does not give way in the smallest 

FIG. 20. 

degree to extension, but when subjected to a pull is 
invariably torn asunder. 

The distribution of the boulders, too, on the surface 
of 'the glacier is readily explained when we take their 
motion into account. These boulders are fragments of 
the mountains between which the glacier flows. Detached 



FIG. 21. 

partly by the weathering of 
the stone, and partly by the 
freezing of water in its crevices, 
they fall, and for the most part 
on the edge of the mass of ice. 
There they either remain ly- 
ing on the surface, or if they 
have originally burrowed in 
the snow, they ultimately re- 
appear in consequence of the 
melting of the superficial 
layers of ice and snow, and 
they accumulate especially 
at the lower end of the gla- 
cier, where more of the ice 
between them has been 
melted. The blocks which are 
gradually borne down to the 
lower end of the glacier are 
sometimes quite colossal in 
size. Solid rocky masses of 
this kind are met with in the 
lateral and terminal moraines, 
which are as large as a two- 
storied house. 

The masses of stone move in 
lines which are always nearly 
parallel to each other and to 
the longitudinal direction of 
the glacier. Those, therefore, 
that are already in the middle 
remain in the middle, and 
those that lie on the edge re- 
main at the edge. These latter 
are the more numerous, for 
during the entire course of the 
glacier, fresh boulders are COD- 


stantly falling on the edge, but cannot fall on the middle. 
Thus are formed on the edge of the mass of ice the lateral 
moraines, the boulders of which partly move along with 
the ice, partly glide over its surface, and partly rest on 
the solid rocky base near the ice. But when two glacier 
streams unite, their coinciding lateral moraines come to 
lie upon the centre of the united ice-stream, and then 
move forward as central moraines parallel to each other 
and to the banks of the stream, and they show, as far 
as the lower end, the boundary-line of the ice which 
originally belonged to one or the other of the arms of the 
glacier. They are very remarkable as displaying in what 
regular parallel bands the adjacent parts of the ice-stream 
glide downwards. A glance at the map of the Mer de 
Glace, and its four central moraines, exhibits this very 

On the Glacier du Geant and its continuation in the 
Mer de Glace, the stones on the surface of the ice 
delineate, in alternately grayer and whiter bands, a kind 
of yearly rings which were first observed by Forbes. 
For since in the cascade at g, Fig. 21, more ice slides 
down in summer than in winter, the surface of the 
ice below the cascade forms a series of terraces as seen 
in the drawing, and as those slopes of the terraces which 
have a northern aspect melt less than their upper plane 
surfaces, the former exhibit purer ice than the latter. 
This, according to Tyndall, is the probable origin of 
these dirt bands. At first they run pretty much across 
the glacier, but as afterwards their centre moves some- 
what more rapidly than the ends, they acquire farther 
down a curved shape, as represented in the map, Fig. 19. 
By their curvature they thus show to the observer with 
what varying velocity ice advances in the different parts 
of its course. 

A very peculiar part is played by certain stones which 


are imbedded in the lower surface of the mass of ice, and 
which have partly fallen there through crevasses, and 
may partly have been detached from the bottom of the 
valley. For these stones are gradually pushed with the 
ice along the base of the valley, and at the same time are 
pressed against this base by the enormous weight of the 
superincumbent ice. Both, the stones imbedded in the 
ice, as well as the rocky base, are equally hard, but by 
their friction against each other they are ground to 
powder with a power compared to which any human 
exertion of force is infinitely small. The product of 
this friction is an extremely fine powder which, swept 
away by water, appears lower down in the glacier brook, 
imparting to it a whitish or yellowish muddy appearance. 

The rocks of the trough of the valley, on the contrary, 
on which the glacier exerts year by year its grinding 
power, are polished as if in an enormous polishing 
machine. They remain as rounded, smoothly polished 
masses, in which are occasional scratches produced by 
individual harder stones. Thus we see them appear at 
the edge of existing glaciers, when after a series of dry 
and hot seasons the glaciers have somewhat receded. 
But we find such polished rocks as remains of gigantic 
ancient glaciers to a far greater extent in the lower 
parts of many Alpine valleys. In the valley of the Aar 
more especially, as far down as Meyringen, the rock-walls 
polished to a considerable height are very characteristic. 
There also we find the celebrated polished plates, over 
which the way passes, and which are so smooth that 
furrows have had to be hewn into them and rails erected 
to enable men and animals to traverse them in safety. 

The former enormous extent of glaciers is recognised 
by ancient moraine-dykes, and by transported blocks of 
stone, as well as by these polished rocks. The blocks of 
stone which have been carried away by the glacier are 


distinguished from those which water has rolled down, 
by their enormous magnitude, by the perfect retention 
of all their edges which are not at all rounded off, and 
finally by their being deposited on the glacier in exactly 
the same order in which the rocks of which they formed 
part stand in the mountain ridge ; while the stones 
which currents of water carry along are completely 
mixed together. 

From these indications, geologists have been able to 
prove that the glaciers of Chamouni, of Monte Rosa, 
of the St. Gotthard, and the Bernese Alps, formerly 
penetrated through the valley of the Arve, the Rhone, 
the Aare, and the Rhine to the more level part of 
Switzerland and the Jura, where they have deposited 
their boulders at a height of more than a thousand feet 
above the present level of the Lake of Neufchatel. 
Similar traces of ancient glaciers are found upon the 
mountains of the British Islands, and upon the Scan- 
dinavian Peninsula. 

The drift-ice too of the Arctic Sea is glacier ice; it 
is pushed down into the sea by the glaciers of Greenland, 
becomes detached from the rest of the glacier, and floats 
away. In Switzerland we find a similar formation of 
drift-ice, though on a far smaller scale, in the little 
Marjelen See, into which part of the ice of the great 
Aletsch Glacier pushes down. Blocks of stone which lie 
in drift-ice may make long voyages over the sea. The vast 
number of blocks of granite which are scattered on the 
North German plains, and whose granite belongs to the 
Scandinavian mountains, has been transported by drift- 
ice at the time when the European glaciers had such an 
enormous extent. 

I must unfortunately content myself with these few 
references to the ancient history of glaciers, and re- 
vert now to the processes at present at work in them. 


From the facts which I have brought before you it 
results that the ice of a glacier flows slowly like the 
current of a very viscous substance, such for instance 
as honey, tar, or thick magma of clay. The mass of 
ice does not merely flow along the ground like a solid 
which glides over a precipice, but it bends and twists in 
itself ; and although even while doing this it moves along 
the base of the valley, yet the parts which are in contact 
with the bottom and the sides of the valley are per- 
ceptibly retarded by the powerful friction ; the middle 
of the surface of the glacier, which is most distant both 
from the bottom and the sides, moving most rapidly. 
Rendu, a Savoyard priest, and the celebrated natural 
philosopher Forbes, were the first to suggest the similarity 
of a glacier with a current of a viscous substance. 

Now you will perhaps enquire with astonishment how 
it is possible that ice, which is the most brittle and 
fragile of substances, can flow in the glacier like a 
viscous mass ; and you may perhaps be disposed to 
regard this as one of the wildest and most improbable 
statements that have ever been made by philosophers. 
I will at once admit that philosophers themselves were 
not a little perplexed by these results of their investiga- 
tions. But the facts were there, and could not be got 
rid of. How this mode of motion originated was for a 
long time quite enigmatical, the more so since the 
numerous crevasses in glaciers were a sufficient indication 
of the well-known brittleness of ice; and as Tyndall 
correctly remarked, this constituted an essential difference 
between a stream of ice and the flow of lava, of tar, of 
honey, or of a current of mud. 

The solution of this strange problem was found, as is 
so often the case in the natural sciences, in apparently 
recondite investigations into the nature of heat, which 
form one of the most important conquests of modern 


physics, and which constitute what is known as the 
'mechanical theory of heat. Among a great number of 
deductions as to the relations of the diverse natural 
forces to each other, the principles of the mechanical 
theory of heat lead to certain conclusions as to the 
dependence of the freezing-point of water on the pressure 
to which ice and water are exposed. 

Everyone knows that we determine that one fixed 
point of our thermometer scale which we call the freez- 
ing-point or zero, by placing the thermometer in a 
mixture of pure water and ice. Water, at any rate 
when in contact with ice, cannot be cooled below zero 
without itself being converted into ice; ice cannot be 
heated above the freezing-point without melting. Ice 
and water can exist in each other's presence at only one 
temperature, the temperature of zero. 

Now, if we attempt to heat such a mixture by a flame 
beneath it, the ice melts, but the temperature of the 
mixture is never raised above that of so long as some 
of the ice remains unmelted. The heat imparted changes 
ice at zero into water at zero, but the thermometer in- 
dicates no increase of temperature. Hence physicists 
say that heat has become latent, and that water contains 
a certain quantity of latent heat beyond that of ice at 
the same temperature. 

On the other hand, when we withdraw more heat from 
the mixture of ice and water, the water gradually freezes ; 
but as long as there is still liquid water, the temperature 
remains at zero. Water at has given up its latent 
heat, and has become changed into ice at 0. 

Now a glacier is a mass of ice which is everywhere 
interpenetrated by water, and its internal temperature 
is therefore everywhere that of the freezing-point. The 
deeper layers, even of the fields of neve, appear on the 
heights which occur in our Alpine chain to have every- 


where the same temperature. For, though the freshly- 
fallen snow of these heights is, for the most part, at a 
lower temperature than that of 0, the first hours of 
warm sunshine melt its surface and form water, which 
trickles into the deeper colder layers, and there freezes, 
until it has throughout been brought to the temperature 
of the freezing-point. This temperature then remains 
unchanged. For, though by the sun's rays the surface 
of the ice may be melted, it cannot be raised above zero, 
and the cold of winter penetrates as little -into the badly- 
conducting masses of snow and ice as it does into our 
cellars. Thus the interior of the masses of neve, as well as 
of the glacier, remains permanently at the melting-point. 

But the temperature at which water freezes may be 
altered by strong pressure. This was first deduced from 
the mechanical theory of heat by James Thomson of 
Belfast, and almost simultaneously by Clausius of Zurich ; 
and, indeed, the amount of this change may be correctly 
predicted from the same reasoning. For each increase 
of a pressure of one atmosphere the freezing-point is 
lowered by the T ^-j- th part of a degree Centigrade. The 
brother of the former, Sir W. Thomson, the celebrated 
Glasgow physicist, made an experimental confirmation 
of this theoretical deduction by compressing in a suit- 
able vessel a mixture of ice and snow. This mixture 
became colder and colder as the pressure was increased, 
and to the extent required by the mechanical theory. 

Now, if a mixture of ice and water becomes colder 
when it is subjected to increased pressure without the 
withdrawal of heat, this can only be effected by some 
free heat becoming latent; that is, some ice in the 
mixture must melt aiad be converted into water. In 
this is found the reason why mechanical pressure can 
influence the freezing-point. You know that ice occu- 


pies more space than the water from which it is formed. 
When water freezes in closed vessels, it can burst not 
only glass vessels, but even iron shells. Inasmuch, there- 
fore, as in the compressed mixture of ice and water some 
of the ice melts and is converted into water, the volume 
of the mass diminishes, and the mass can yield more to 
the pressure upon it than it could have done without 
such an alteration of the freezing-point. Pressure fur- 
thers in this case, as is usual in the interaction of various 
natural forces, the occurrence of a change, that is fusion, 
which is favourable to the development of its own 

In Sir W. Thomson's experiments, water and ice were 
confined in a closed vessel, from which nothing could 
escape. The case is somewhat different when, as with 
glaciers, the water disseminated in the compressed ice can 
escape through fissures. The ice is then compressed, 
but not the water which escapes. The compressed ice 
becomes colder in conformity with the lowering of its 
freezing-point by pressure; but the freezing-point of 
water which is not compressed is not lowered. Thus 
under these circumstances we have ice colder than in 
contact with water at 0. The consequence is that 
around the compressed ice water continually freezes and 
forms new ice, while on the other hand part of the com- 
pressed ice melts. 

This occurs, for instance, when only two pieces of ice 
are pressed against each other. By the water which 
freezes at their surfaces of contact they are firmly joined 
into one coherent piece of ice. With powerful pressure, 
and the chilling therefore great, this is quickly effected ; 
but even with a feeble pressure it takes place, if suffi- 
cient time be given. Faraday, who discovered this pro- 
perty, called it the regelation of ice; the explanation 


of this phenomenon has been much controverted ; I 
have detailed to you that which I consider most satis- 

This freezing together of two pieces of ice is very 
readily effected by pieces of any shape, which must not, 
however, be at a lower temperature than 0, and the 
experiment succeeds best when the pieces are already in 
the act of melting. 1 They need only be strongly pressed 
together for a few minutes to make them adhere. The 
more plane are the surfaces in contact, the more com- 
plete is their union. But a very slight pressure is suffi- 
cient if the two pieces are left in contact for some time. 2 

This property of melting ice is also utilised by boys in 
making snow-balls and snow-men. It is well known that 
this only succeeds either when the snow is already melt- 
ing, or at any rate is only so much lower than that 
the warmth of the hand is sufficient to raise it to this 
temperature. Very cold snow is a dry loose powder 
which does not stick together. 

The process which children carry out on a small scale 
in making snow-balls, takes place in glaciers on the very 
largest scale. The deeper layers of what was originally 
fine loose neve are compressed by the huge masses rest- 
ing on them, often amounting to several hundred feet, 
and under this pressure they cohere with an ever firmer 
and closer structure. The freshly-fallen snow originally 
consisted of delicate microscopically fine ice spicules, 
united and forming delicate six-rayed, feathery stars of 
extreme beauty. As often as the upper layers of the 
snow-fields are exposed to the sun's rays, some of the 
snow melts ; water permeates the mass, and on reaching 

1 In the Lecture a series of small cylinders of ice, which had been pre- 
pared by a method to be afterwards described, were pressed with their plane 
ends against each other, and thus a cylindrical bar of ice produced. 

8 Vide the additions at the end of this Lecture. 



the lower layers of still colder snow, it again freezes ; 
thus it is that the firn first becomes granular and ac- 
quires the temperature of the freezing-point. But as the 
weight of the superincumbent masses of snow continually 
increases by the firmer adherence of its individual granules, 
it ultimately changes into a dense and perfectly hard 

This transformation of snow into ice may be artificially 
effected by using a corresponding pressure. 

We have here (Fig. 22) a cylindrical cast-iron vessel, 
A A ; the base, B B, is 
held by three screws, and 
can be detached, so as to 
remove the cylinder of ice 
which is formed. After 
the vessel has lain for a 
while in ice-water, so as 
to reduce it to the tem- 
perature of 0, it is 
packed full of snow, and 
then the cylindrical plug, 
C C, which fits the inner 
aperture, but moves in it 
with gentle friction, is 
forced in with the aid of 
an hydraulic press. The 
press used was such that 
the pressure to which the 
snow was exposed could 
be increased to fifty atmospheres. Of course the looser 
snow contracts to a very small volume under such a 
powerful pressure. The pressure is removed, the cylin- 
drical plug taken out, the hollow again filled up with 
snow, and the process repeated until the entire form is 
filled with the mass of ice, which no longer gives way 


to pressure. The compressed snow which I now take out, 
you will see, has been transformed into a hard, angular, 
and translucent cylinder of ice ; and how hard it is, 
appears from the crash which ensues when I throw it to 
the ground. Just as the loose snow in the glaciers is 
pressed together to solid ice, so also in many places 
ready-formed irregular pieces of ice are joined and form 
clear and compact ice. This is most remarkable at the 
base of the glacier cascades. These are glacier falls 
where the upper part of the glacier ends at a steep rocky 
wall, and blocks of ice shoot down as avalanches over the 
edge of this wall. The heap of shattered blocks of ice 
which accumulate become joined at the foot of the rock- 
wall to a compact, dense mass, which then continues its 
way downwards as glacier. More frequent than such cas- 
cades, where the glacier-stream is quite dissevered, are 
places where the base of the valley has a steeper slope, 
as, for instance, the places in the Mer de Glace (Fig. 14), 
at g, of the Cascade of the Glacier du Geant, and at i and 
h of the great terminal cascade of the Glacier des Bois. 
The ice splits there into thousands of banks and cliffs, 
which then recombine towards the bottom of the steeper 
slope and form a coherent mass. 

This also we may imitate in our ice-mould. Instead of 
the snow I take irregular pieces of ice, press them to- 
gether ; add new pieces of ice, press them again, and so 
on, until the mould is full. When the mass is taken 
out it forms a compact coherent cylinder of tolerably clear 
ice, which has a perfectly sharp edge, and is an accurate 
copy of the mould. 

This experiment, which was first made by Tyndall, shows 
that a block of ice may be pressed into any mould just 
like a piece of wax. It might, perhaps, be thought that 
such a block had, by the pressure in the interior, been 
first reduced to powder so fine that it readily penetrated 


every crevice of the mould, and then that this powdered 
ice, like snow, was again combined by freezing. This sug- 
gests itself the more readily, since while the press is being 
worked a continual creaking and cracking is heard in the 
interior of the mould. Yet the mere aspect of the cylin- 
ders pressed from blocks of ice shows us that it has not 
been formed in this manner ; for they are generally clearer 
than the ice which is produced from snow, and the indi- 
vidual larger pieces of ice which have been used to pro- 
duce them are recognised, though they are somewhat 
changed and flattened. This is most beautiful when 
clear pieces of ice are laid in the form and the rest of 
the space stuffed full of snow. The cylinder is then seen 
to consist of alternate layers of clear and opaque ice, the 
former arising from the pieces of ice, and the latter from 
the snow ; but here also the pieces of ice seem pressed 
into flat discs. 

These observations teach, then, that ice need not be 
completely smashed to fit into the prescribed mould, but 
that it may give way without losing its coherence. This 
can be still more completely proved, and we can acquire a 
still better insight into the cause of the pliability of ice, 
if we press the ice between two plane wooden boards, 
instead of in the mould, into which we cannot see. 

I place first an irregular cylindrical piece of natural 
ice, taken from the frozen surface of the river, with its 
two plane terminal surfaces between the plates of the 
press. If I begin to work, the block is broken by 
pressure ; every crack which forms extends through 
the entire mass of the block ; this splits into a heap of 
larger fragments, which again crack and are broken the 
more the press is worked. If the pressure is relaxed, all 
these fragments are, indeed, reunited by freezing, but 
the aspect of the whole indicates that the shape of the 
block has resulted less from pliability than from fracture, 



and that the individual fragments have completely altered 
their mutual positions. 

The case is quite different when one of the cylinders 
which we have formed from snow or ice is placed between 
tho plates of the press. As the press is worked the creaking 
and cracking is heard, but it does not break ; it gradually 
changes its shape, becomes lower and at the same time 
thicker ; and only when it has been changed into a tole- 
rably flat circular disc does it begin to give way at the 
edges and form cracks, like crevasses on a small scale. 
Fig. 23 shows the height and diameter of such a cylinder 
in its original condition ; Fig. 24 represents its appearance 
after the action of the press. 

FIG. 24. 

A still stronger proof of the pliability of ice is afforded 
when one of our cylinders is forced through a narrow aper- 
ture. With this view I place a base on the previously 
described mould, which has a conical perforation, the 
external aperture of which is only two-thirds the dia- 
meter of the cylindrical aperture of the form. Fig. 25 
gives a section of the whole. If now I insert into this 
one of the compressed cylinders of ice, and force down the 
plug a, the ice is forced through the narrow aperture in 



FIG. 25. 

the base. It at first emerges as a solid cylinder of the 
same diameter as the aper- 
ture ; but as the ice follows 
more rapidly in the centre 
than at the edges, the free 
terminal surface of the 
cylinder becomes curved, 
the end thickens, so that it 
could not be brought back 
through the aperture, and 
it ultimately splits off. Fig. 
26 exhibits a series of 
shapes which have resulted 
in this manner. 1 

Here also the cracks in the emerging cylinder of ice 
exhibit a surprising similarity with the longitudinal rifts 

FIG. 26. 

which divide a glacier current where it presses through a 
narrow rocky pass into a wider valley. 

In the cases which we have described we see the change 
in shape of the ice taking place before our eyes, whereby 
the block of ice retains its coherence without breaking 
into individual pieces. The brittle mass of ice seems 
rather to yield like a piece of wax. 

A closer inspection of a clear cylinder of ice compressed 

1 In this experiment the lower temperature of the compressed ice some- 
times extended so far through the iron form, that the water in the slit 
between the base plate and the cylinder froze and formed a thin sheet of ice, 
although the pieces of ice as well as the iron mould had previously laid in 
ice-water, and could not be colder than 0. 


from clear pieces of ice, wliile the pressure is being applied, 
shows us what takes place in the interior ; for we then see 
an innumerable quantity of extremely fine radiating cracks 
shoot through it like a turbid cloud, which mostly dis- 
appear, though not completely, the moment the pressure 
is suspended. Such a compressed block is distinctly 
more opaque immediately after the experiment than it 
was before ; and the turbidity arises, as may easily be 
observed by means of a lens, from a great number 
of whitish capillary lines crossing the interior of the 
mass of what is otherwise clear. These lines are the 
optical expression of extremely fine cracks l which inter- 
penetrate the mass of the ice. Hence we may conclude 
that the compressed block is traversed by a great num- 
ber of fine cracks and fissures, which render it pliable ; 
that its particles become a little dispersed, and are there- 
fore withdrawn from pressure, and that immediately after- 
wards the greater part of the fissures disappear, owing to 
their sides freezing. Only in those places in which the 
surfaces of the small displaced particles do not accurately 
fit to each other some fissured spaces remain open, and are 
discovered as white lines and surfaces by the reflection of 
the light. 

These cracks and laminae also become more perceptible 
when the ice which, as I before mentioned, is below zero 
immediately after pressure has been applied is again 
raised to this temperature and begins to melt. The cre- 

1 These cracks are probably quite empty and free from air, for they are 
also formed when perfectly clear and air-free pieces of ice are pressed in 
the form which has been previously filled with water, and where, therefore, 
no air could gain access to the pieces of ice. That such air-free crevices 
occur in glacier ice has been already demonstrated by Tyndall. When the 
compressed ice afterwards melts, these crevices fill up with water, no air 
being left. They are then, however, far less visible, and the whole block 
is therefore clearer. And just for this reason they could not originally 
have been filled with water. 


vices then fill with water, and such ice then consists of a 
quantity of minute granules from the size of a pin's head 
to that of a pea, which are closely pushed into one another 
at the edges and projections, and in part have coalesced, 
while the narrow fissures between them are full of water. 
A block of ice thus formed of ice-granules adheres firmly 
together ; but if particles be detached from its corners 
they are seen to consist of these angular granules. Gla- 
cier ice, when it begins to melt, is seen to possess the 
same structure, except that the pieces of which it consists 
are mostly larger than in artificial ice, attaining the size 
of a pigeon's egg. 

Glacier ice and compressed ice are thus seen to be sub- 
stances of a granular structure, in opposition to regularly 
crystallised ice, such as is formed on the surface of still 
water. We here meet with the same differences as be- 
tween calcareous spar and marble, both of which consist 
of carbonate of lime ; but while the former is in large, 
regular crystals, the latter is made up of irregularly 
agglomerated crystalline grains. In calcareous spar, as 
well as in crystallised ice, the cracks produced by inserting 
the point of a knife extend through the mass, while in 
granular ice a crack which arises in one of the bodies 
where it must yield does not necessarily spread beyond 
the limits of the granule. 

Ice which has been compressed from snow, and has 
thus from the outset consisted of innumerable very fine 
crystalline needles, is seen to be particularly plastic. 
Yet in appearance it materially differs from glacier ice, 
for it is very opaque, owing to the great quantity of air 
which was originally enclosed in the flaky mass of snow, 
and which remains there as extremely minute bubbles. 
It can be made clearer by pressing a cylinder of such ice 
between wooden boards ; the air-bubbles appear then on 
the top of the cylinder as a light foam. If the discs are 


again broken, placed in the mould, and pressed into a 
cylinder, the air may gradually be more and more elimi- 
nated, and the ice be made clearer. No doubt in glaciers 
the originally whitish mass of neve is thus gradually 
transformed into the clear, transparent ice of the glacier. 

Lastly, when streaked cylinders of ice formed from 
pieces of snow and ice are pressed into discs, they become 
finely streaked, for both their clear and their opaque layers 
are uniformly extended. 

Ice thus striated occurs in numerous glaciers, and is 
no doubt caused, as Tyndall maintains, by snow falling 
between the blocks of ice ; this mixture of snow and clear 
ice is again compressed in the subsequent path of the 
glacier, and gradually stretched by the motion of the 
mass : a process quite analogous to the artificial one which 
we have demonstrated. 

Thus to the eye of the natural philosopher the glacier, 
with its wildly-heaped ice-blocks, its desolate, stony, and 
muddy surface, and its threatening crevasses, has become 
a majestic stream whose peaceful and regular flow has no 
parallel ; which, according to fixed and definite laws, nar- 
rows, expands, is heaped up, or, broken and shattered, 
falls down precipitous heights. If we trace it beyond its 
termination we see its waters, uniting to a copious brook, 
burst through its icy gate and flow away. Such a brook, 
on emerging from the glacier, seems dirty and turbid 
enough, for it carries away as powder the stone which 
the glacier has ground. We are disenchanted at seeing 
the wondrously beautiful and transparent ice converted 
into such muddy water. But the water of the glacier 
streams is as pure and beautiful as the ice, though its 
beauty is for the moment concealed and invisible. We 
must search for these waters after they have passed 
through a lake in which they have deposited this pow- 
dered stone. The Lakes of Geneva, of Thun, of Lucerne, 


of Constance, the Lago Maggiore, the Lake of Como, and 
the Lago di Garda are chiefly fed with glacier waters ; 
their clearness and their wonderfully beautiful blue or 
blue-green colour are the delight of all travellers. 

Yet, leaving aside the beauty of these waters, and con- 
sidering only their utility, we shall have still more reason 
for admiration. The unsightly mud, which the glacier 
streams wash away, forms a highly fertile soil in the 
places where it is deposited ; for its state of mechanical 
division is extremely fine, and it is moreover an utterly 
unexhausted virgin soil, rich in the mineral food of plants. 
The fruitful layers of fine loam which extend along the 
whole Khine plain as far as Belgium, and are known as 
Loess, are nothing more than the dust of ancient glaciers* 

Then, again, the irrigation of a district, which is effected 
by the snow-fields and glaciers of the mountains, is distin- 
guished from that of other places by its comparatively 
greater abundancy, for the moist air which is driven over 
the cold mountain peaks deposits there most of the water 
it contains in the form of snow. In the second place, the 
snow melts most rapidly in summer, and thus the springs 
which flow from the snow-fields are most abundant in that 
season of the year in which they are most needed. 

Thus we ultimately get to know the wild, dead ice- 
wastes from another point of view. From them trickles 
in thousands of rills, springs, and brooks the fructifying 
moisture which enables the industrious dwellers of the 
Alps to procure succulent vegetation and abundance of 
nourishment from the wild mountain slopes. On the 
comparatively small surface of the Alpine chain they 
produce the mighty streams, the Rhine, the Rhone, the 
Po, the Adige, the Inn, which for hundreds of miles form 
broad, rich river-valleys, extending through Europe to the 
German Ocean, the Mediterranean, the Adriatic, and the 
Black Sea. Let us call to mind how magnificently Goethe, 


in c Mahomet's Song,' has depicted the course of the rocky 
spring, from its origin beyond the clouds to its union 
with Father Ocean. It would be presumptuous after him 
to give such a picture in other than his own words : 

And along, in triumph rolling, 
Names he gives to regions ; cities 
Grow amain beneath his feet. 

On and ever on he rushes ; 
Spire and turret fiery crested, 
Marble palaces, the creatures 
Of his wealth, he leaves behind. 

Pine-built houses bears the Atlas 
On his giant shoulders. O'er his 
Head a thousand pennons rustle, 
Floating far upon the breezes, 
Tokens of his majesty. 

And so beareth he his brothers, 
And his treasures, and his children, 
To their primal sire expectant, 
All his bosom throbbing, heaving 
With a wild tumultuous joy. 




THE theory of the regelation of ice has led to scientific discussions 
between Faraday and Tyndall on the one hand, and James and 
Sir W. Thomson on the other. In the text I have adopted the 
theory of the latter, and must now accordingly defend it. 

Faraday's experiments show that a very slight pressure, not 
more than that produced by the capillarity of the layer of water 
between two pieces of ice, is sufficient to freeze them together. 
James Thomson observed that in Faraday's experiments, pres- 
sure which could freeze them together was not utterly wanting. 
I have satisfied myself by my own experiments that only very 
slight pressure is necessary. It must, however, be remembered, 
that the smaller the pressure the longer will be the time required 
to freeze the two pieces, and that then the junction will be very 
narrow and very fragile. Both these points are readily explicable 
on Thomson's theory. For under a feeble pressure the difference 
in temperature between ice and water will be very small, and 
the latent heat will only be slowly abstracted from the layers of 
water in contact with the pressed parts of the ice, so that a long 
time is necessary before they freeze. We must further take into 
account that we cannot in general consider that the two surfaces 
are quite in contact ; under a feeble pressure which does not 
appreciably alter their shape, they will only touch in what are 
practically three points. A feeble total pressure on the pieces of 
ice concentrated on such narrow surfaces will always produce a 
tolerably great local pressure under the influence of which some 
ice will melt, and the water thus formed will freeze. But the 
bridge which joins them will never be otherwise than narrow. 

Under stronger pressure, which may more completely alter 
the shape of the pieces of ice, and fit them against each other, 
and which will melt more of the surfaces that are first in con- 
tact, there will be a greater difference between the temperature 
of the ice and water, and the bridges will be more rapidly 
formed, and be of greater extent. 


In order to show the slow action of the small differences of 
temperature which here come into play, I made the following 

A glass flask with a drawn-out neck was half filled with 
water, which was boiled until all the air in the flask was driven 
out. The neck of the flask was then hermetically sealed. When 
cooled, the flask was void of air, and the water within it freed 
from the pressure of the atmosphere. As the water thus pre- 
pared can be cooled considerably below C. before the first ice 
is formed, while when ice is in the flask it freezes at C., the 
flask was in the first instance placed in a freezing mixture until 
the water was changed into ice. It was afterwards permitted to 
melt slowly in a place, the temperature of which was + 2 C., 
until the half of it was liquefied. 

The .flask thus half filled with water, having a disc of ice 
swimming upon it, was placed in a mixture of ice and water, 
being quite surrounded by the mixture. After an hour, the 
disc within the flask was frozen to the glass. By shaking the 
flask the disc was liberated, but it froze again. This occurred 
as often as the shaking was repeated. 

The flask was permitted to remain for eight days in the 
mixture, which was kept throughout at a temperature of C. 
During this time a number of very regular and sharply defined 
ice-crystals were ibrmed, and augmented very slowly in size. 
This is perhaps the best method of obtaining beautifully formed 
crystals of ice. 

While, therefore, the outer ice which had to support the 
pressure of the atmosphere slowly melted, the water within the 
flask, whose freezing-point, on account of a defect of pressure, 
was 0-0075 C. higher, deposited crystals of ice. The heat 
abstracted from the water in this operation had, moreover, to 
pass through the glass of the flask, which, together with the 
small difference of temperature, explains the slowness of the 
freezing process. 

Now as the pressure of one atmosphere on a square milli- 
metre amounts to about ten grammes, a piece of ice weighing 
ten grammes, which lies upon another and touches it in three 
places, the total surface of which is a square millimetre, will 
produce on these surfaces a pressure of an atmosphere, Ice will 


therefore be formed more rapidly in the surrounding water than 
it was in the flask, where the side of the glass was interposed 
between the ice. and the water. Even with a much smaller 
weight the same result will follow in the course of an hour. 
The broader the bridges become, owing to the freshly formed 
ice, the greater will be the surfaces over which the pressure 
exerted by the upper piece of ice is distributed, and the feebler 
it will become ; so that with such feeble pressure the bridges 
can only slowly increase, and therefore they will be readily 
broken when we try to separate the pieces. 

It cannot, moreover, be doubted, that in Faraday's experi- 
ments, in which two perforated discs of ice were placed in con- 
tact on a horizontal glass rod, so that gravity exerted no pressure, 
capillary attraction is sufficient to produce a pressure of some 
grammes between the plates, and the preceding discussions show 
that such a pressure, if adequate time be given, can form bridges 
between the plates. 

If, on the other hand, two of the above-described cylinders of 
ice are powerfully pressed together by the hands, they adhere in 
a few minutes so firmly, that they can only be detached by the 
exertion of a considerable force, for which indeed that of the 
hands is sometimes inadequate. 

In my experiments I found that the force and rapidity with 
which the pieces of ice united were so entirely proportional to 
the pressure, that I cannot but assign this as the actual and 
sufficient cause of their union. 

In Faraday's explanation, according to which regelation is due 
to a contact action of ice and water, I find a theoretical difficulty. 
By the water freezing, a considerable quantity of latent heat 
must be set free, and it is not clear what becomes of this. 

Finally, if ice in its change into water passes through an inter- 
mediate viscous condition, a mixture of ice and water which was 
kept for days at a temperature of must ultimately assume 
this condition in its entire mass, provided its temperature was 
uniform throughout ; this however is never the case. 

As regards what is called the plasticity of ice, James Thomson 
has given an explanation of it in which the formation of cracks 
in the interior is not presupposed. No doubt when a mass of ice 
in different parts of the interior is exposed to different pressures, 


u portion of the more powerfully compressed ice will melt ; and 
the latent heat necessary for this will be supplied by the ice 
which is less strongly compressed, and by the water in contact 
with it. Thus ice would melt at the compressed places, and water 
would freeze in those which are not pressed : ice would thus be 
gradually transformed and yield to pressure. It is also clear 
that, owing to the very small conductivity for heat which ice 
possesses, a process of this kind must be extremely slow, if the 
compressed and colder layers of ice, as in glaciers, are at con- 
siderable distances from the less compressed ones, and from the 
water which furnishes the heat for melting. 

To test this hypothesis, I placed in a cylindrical vessel, between 
two discs of ice of three inches in diameter, a smaller cylindrical 
piece of an inch in diameter. On the uppermost disc I placed a 
wooden disc, and this I loaded with a weight of twenty pounds. 
The section of the narrow piece was thus exposed to a pressure 
of more than an atmosphere. The whole vessel was packed 
between pieces of ice, and left for five days in a room, the tem- 
perature of which was a few degrees above the freezing-point. 
Under these circumstances the ice in the vessel, which was ex- 
posed to the pressure of the weight, should melt, and it might be 
expected that the narrow cylinder on which the pressure was 
most powerful should have been most melted. Some water was 
indeed formed in the vessel, but mostly at the expense of the 
larger discs at the top and bottom, which being nearest the 
outside mixture of ice and water could acquire heat through the 
sides of the vessel. A small welt, too, of ice, was formed round 
the surface of contact of the narrower with the lower broad 
piece, which showed that the water, which had been formed in 
consequence of the pressure, had again frozen in places in which 
the pressure ceased. Yet under these circumstances there was 
no appreciable alteration in the shape of the middle piece which 
was most compressed. 

This experiment shows, that although changes in the shape of 
the pieces of ice must take place in the course of time in accord- 
ance with J. Thomson's explanation, by which the more strongly 
compressed parts melt, and new ice is formed at the places which 
are freed from pressure, these changes must be extremely slow 
when the thickness of the pieces of ice through which the heat 


is conducted is at all considerable. Any marked change in 
shape by melting in a medium the temperature of which is 
everywhere 0, could not occur without access of external heat, 
or from the uncompressed ice and water ; and with the small 
differences in temperature which here come into play, and from 
the badly conducting power of ice, it must be extremely slow. 

That on the other hand, especially in granular ice, the forma- 
tion of cracks, and the displacement of the surfaces of those 
cracks, render such a change of form possible, is shown by the 
above-described experiments on pressure ; and that in glacier 
ice changes of form thus occur, follows from the banded struc- 
ture, and the granular aggregation which is manifest on melting, 
and also from the manner in which the layers change their 
position when moved, and so forth. Hence, I doubt not that 
Tyndall has discovered the essential and principal cause of the 
motion of glaciers, in referring it to the formation of cracks and 
to regelation. 

I would at the same time observe that a quantity of heat, 
which is far from inconsiderable, must be produced by 
friction in the larger glaciers. It may be easily shown by 
calculation, that when a mass of firn moves from the Col du 
Geant to the source of the Arveyron, the heat due to the mecha- 
nical work would be -sufficient to melt a fourteenth part of the 
mass. And as the friction must be greatest in those places that 
are most compressed, it will at any rate be sufficient to remove 
just those parts of the ice which offer most resistance to motion. 

I will add in conclusion, that the above-described granular 
structure of ice is beautifully shown in polarised light. If a 
small clear piece is pressed in the iron mould, so as to form a 
disc of about five inches in thickness, this is sufficiently trans- 
parent for investigation. Viewed in the polarising apparatus, a 
great number of variously coloured small bands and rings are 
seen in the interior ; and by the arrangement of their colours it 
is easy to recognise the limits of the ice-granules, which, heaped 
on one another in irregular order of their optical axes, constitute 
the plate. The appearance is essentially the same when the 
plate has just been taken out of the press, and the cracks appear 
in it as whitish lines, as afterwards when these crevices have 
been filled up in consequence of the ice beginning to melt. 


In order to explain the continued coherence of the piece of 
ice during its change of form, it is to be observed that in general 
the cracks in the granular ice are only superficial, and do not 
extend throughout its entire mass. This is directly seen during 
the pressing of the ice. The crevices form and extend in dif- 
ferent directions, like cracks produced by a heated wire in a 
glass tube. Ice possesses a certain degree of elasticity, as may 
be seen in a thin flexible plate. A fissured block of ice of tRis 
kind will be able to undergo a displacement at the two sides 
which form the crack, even when these continue to adhere in the 
unfissured part of the block. If then part of the fissure at first 
formed is closed by regelation, the fissure can extend in the 
opposite direction without the continuity of the block being at 
any time disturbed. It seems to me doubtful, too, whether in 
compressed ice and in glacier ice, which apparently consists of 
interlaced polyhedral granules, these granules, before any at- 
tempt is made to separate them, are completely detached from 
each other, and are not rather connected by ice bridges which 
readily give way ; and whether these latter do not produce the 
comparatively firm coherence of the apparent heap of granules. 

The properties of ice here described are interesting from a 
physical point of view, for they enable us to follow so closc-ly 
the transition from a crystalline body to a granular one ; and 
they give the causes of the alteration of its properties better 
than in any other well-known example. Most natural substances 
show no regular crystalline structure ; our theoretical ideas refer 
almost exclusively to crystallised and perfectly elastic bodies. 
It is precisely in this relationship that the transition from fragile 
and elastic crystalline ice into plastic granular ice is so very- 




A NEW conquest of very general interest has been recently 
made by natural philosophy. In the following pages I 
will endeavour to give an idea of the nature of this con- 
quest. It has reference to a new and universal natural 
law, which rules the action of natural forces in their 
mutual relations towards each other, and is as influential 
on our theoretic views of natural processes as it is im- 
portant in their technical applications. 

Among the practical arts which owe their progress to 
the development of the natural sciences, from the con- 
clusion of the middle ages downwards, practical mechanics, 
aided by the mathematical science which bears the same 
name, was one of the most prominent. The character of 
the art was, at the time referred to, naturally very dif- 
ferent from its present one. Surprised and stimulated by 
its own success, it thought no problem beyond its power, 
and immediately attacked some of the most difficult and 
complicated. Thus it was attempted to build automaton 
figures which should perform the functions of men and 


animals. The marvel of the last century was Vaucanson's 
duck, which fed and digested its food ; the flute-player of 
the same artist, which moved all its fingers correctly ; the 
writing- boy of the elder, and the pianoforte-player of the 
younger Droz ; which latter, when performing, followed its 
hands with its eyes, and at the conclusion of the piece 
bowed courteously to the audience. That men like those 
mentioned, whose talent might bear comparison with the 
most inventive heads of the present age, should spend so 
much time in the construction of these figures which we 
at present regard as the merest trifles, would be incom- 
prehensible, if they had not hoped in solemn earnest to 
solve a great problem. The writing-boy of the elder 
Droz was publicly exhibited in Germany some years ago. 
Its wheel work is so complicated, that no ordinary head 
would be sufficient to decipher its manner of action. 
When, however, we are informed that this boy and its 
constructor, being suspected of the black art, lay for a 
time in the Spanish Inquisition, and with difficulty ob- 
tained their freedom, we may infer that in those days 
even such a toy appeared great enough to excite doubts 
as to its natural origin. And though these artists may 
not have hoped to breathe into the creature of their in- 
genuity a soul gifted with moral completeness, still there 
were many who would be willing to dispense with the 
moral qualities of their servants, if at the same time 
their immoral qualities could also be got rid of; and 
to accept, instead of the mutability of flesh and bones, ser- 
vices which should combine the regularity of a machine 
with the durability of brass and steel. 

The object, therefore, which the inventive genius of the 
past century placed before it with the fullest earnestness, 
and not as a piece of amusement merely, was boldly chosen, 
and was followed up with an expenditure of sagacity which 
has contributed not a little to enrich the mechanical 


experience which a later time knew how to take advan- 
tage of. We no longer seek to build machines which 
shall fulfil the thousand services required of one man, 
but desire, on the contrary, that a machine shall perform 
one service, and shall occupy in doing it the place of a 
thousand men. 

From these efforts to imitate living creatures, another 
idea, also by a misunderstanding, seems to have developed 
itself, and which, as it were, formed the new philosopher's 
stone of the seventeenth and eighteenth centuries. It 
was now the endeavour to ..construct a perpetual motion. 
Under this term was understood a machine, which, 
without being wound up, without consuming in the 
working of it falling water, wind, or any other natural 
force, should still continue in motion, the motive power 
being perpetually supplied by the machine itself. Beasts 
and human beings seemed to correspond to the idea of 
such an apparatus, for they moved themselves ener- 
getically and incessantly as long as they lived, and 
were never wound up ; nobody set them in motion. A 
connexion between the supply of nourishment and the 
development of force did not make itself apparent. The 
nourishment seemed only necessary to grease, as it 
were, the wheelwork of the animal machine, to replace 
what was used up, and to renew the old. The develop- 
ment of force out of itself seemed to be the essential 
peculiarity, the real quintessence of organic life. If, 
therefore, men were to be constructed, a perpetual motion 
must first be found. 

Another hope also seemed to take up incidentally the 
second place, which in our wiser age would certainly have 
claimed the first rank in the thoughts of men. The per- 
petual motion was to produce work inexhaustibly without 
corresponding consumption, that is to say, out of nothing. 
Work, however, is money. Here, therefore, the great 


practical problem which the cunning heads of all cen- 
turies have followed in the most diverse ways, namely, to 
fabricate money out of nothing, invited solution. The 
similarity with the philosopher's stone sought by the 
ancient chemists was complete. That also was thought 
to contain the quintessence of organic life, and to be 
capable of producing gold. 

The spur which drove men to inquiry was sharp, and 
the talent of some of the seekers must not be estimated 
as small. The nature of the problem was quite calcu- 
lated to entice poring brains, to lead them round a circle 
for years, deceiving ever with new expectations which 
vanished upon nearer approach, and finally reducing these 
dupes of hope to open insanity. The phantom could not 
be grasped. It would be impossible to give a history of 
these efforts, as the clearer heads, among whom the elder 
Droz must be ranked, convinced themselves of the futility 
of their experiments, and were naturally not inclined to 
speak much about them. Bewildered intellects, however, 
proclaimed often enough that they had discovered the 
grand secret ; and as the incorrectness of their proceed- 
ings was always speedily manifest, the matter fell into bad 
repute, and the opinion strengthened itself more and 
more that the problem was not capable of solution ; one 
difficulty after another was brought under the dominion 
of mathematical mechanics, and finally a point was 
reached where it could be proved, that at least by the use 
of pure mechanical forces no perpetual motion could be 

We have here arrived at the idea of the driving force 
or power of a machine, and shall have much to do with it 
in future. I must therefore give an explanation of it. 
The idea of work is evidently transferred to machines by 
comparing their performances with those of men and 
animals, to replace which they were applied. We still 


reckon the work of steam-engines according to horse- 
power. The value of manual labour is determined partly 
by the force which is expended in it (a strong labourer is 
valued more highly than a weak one), partly, however, 
by the skill which is brought into action. Skilled work- 
men are not to be had in any quantity at a moment's 
notice ; they must have both talent and instruction, their 
education requires both time and trouble. A machine, 
on the contrary, which executes work skilfully, can always 
be multiplied to any extent ; hence its skill has not the 
high value of human skill in domains where the latter 
cannot be supplied by machines. Thus the idea of the 
quantity of work in the case of machines has been limited 
to the consideration of the expenditure of force ; this was 
the more important, as indeed most machines are con- 
structed for the express purpose of exceeding, by the mag- 
nitude of their effects, the powers of men and animals. 
Hence, in a mechanical sense, the idea of work has become 
identical with that of the expenditure of force, and in 
this way I will apply it in the following pages. 

How, then, can we measure this expenditure, and com- 
pare it in the case of different machines ? 

I must here conduct you a portion of the way as 
short a portion as possible over the uninviting field of 
mathematico-mechanical ideas, in order to bring you to 
a point of view from which a more rewarding prospect 
will open. And though the example which I will here 
choose, namely, that of a water-mill with iron hammer, 
appears to be tolerably romantic, still, alas ! I must leave 
the dark forest valley, the foaming brook, the spark- 
emitting anvil, and the black Cyclops wholly out of sight, 
and beg a moment's attention for the less poetic side of 
the question, namely, the machinery. This is driven by a 
water-wheel, which in its turn is set in motion by the 
falling water. The axle of the water-wheel has at certain 


places small projections, thumbs, which, during the rota- 
tion, lift the heavy hammer and permit it to fall again. 
The falling hammer belabours the mass of metal, which 
is introduced beneath it. The work therefore done by 
the machine consists, in this case, in the lifting of the 
hammer, to do which the gravity of the latter must be 
overcome. The expenditure of force will in the first 
place, other circumstances being equal, be proportional 
to the weight of the hammer; it will, for example, be 
double when the weight of the hammer is doubled. But 
the action of the hammer depends not upon its weight 
alone, but also upon the height from which it falls. If 
it falls through two feet, it will produce a greater effect 
than if it falls through only one foot. It is, however, 
clear that if the machine, with a certain expenditure of 
force, lifts the hammer a foot in height, the same amount 
of force must be expended to raise it a second foot in 
height. The work is therefore not only doubled when 
the weight of the hammer is increased twofold, but also 
when the space through which it falls is doubled. From 
this it is easy to see that the work must be measured by 
the product of the weight into the space through which 
it ascends. And in this way, indeed, we measure in 
mechanics. The unit of work is a foot-pound, that is, a 
pound weight raised to the height of one foot. 

While the work in this case consists in the raising of 
the heavy hammer-head, the driving force which sets the 
latter in motion is generated by falling water. It is not 
necessary that the water should fall vertically, it can also 
flow in a moderately inclined bed ; but it must always, 
where it has water-mills to set in motion, move from a 
higher to a lower position. Experiment and theory 
concur in teaching, that when a hammer of a hundred- 
weight is to be raised one foot, to accomplish this at 
least a hundredweight of water must fall through the 


space of one foot ; or what is equivalent to this, two 
hundredweight must fall half a foot, or four hundred- 
weight a quarter of a foot, &c. In short, if we multiply 
the weight of the falling water by the height through 
which it falls, and regard, as before, the product as the 
measure of the work, then the work performed by the 
machine in raising the hammer can, in the most favour- 
able case, be only equal to the number of foot-pounds of 
water which have fallen in the same time. In practice, 
indeed, this ratio is by no means attained : a great portion 
of the work of the falling water escapes unused, inasmuch 
as part of the force is willingly sacrificed for the sake of 
obtaining greater speed. 

I will further remark, that this relation remains un- 
changed whether the hammer is driven immediately by 
the axle of the wheel, or whether by the intervention 
of wheelwork, endless screws, pulleys, ropes the motion 
is transferred to the hammer. We may, indeed, by such 
arrangements succeed in raising a hammer of ten hun- 
dredweight, when by the first simple arrangement the 
elevation of a hammer of one hundredweight might alone 
be possible ; but either this heavier hammer is raised to 
only one-tenth of the height, or tenfold the time is 
required to raise it to the same height ; so that, however 
we may alter, by the interposition of machinery, the 
intensity of the acting force, still in a certain time, 
during which the mill-stream furnishes us with a definite 
quantity of water, a certain definite quantity of work, and 
no more, can be performed. 

Our machinery, therefore, has in the first place done 
nothing more than make use of the gravity of the falling 
water in order to overpower the gravity of the hammer, 
and to raise the latter. When it has lifted the hammer 
to the necessary height, it again liberates it, and the 
hammer falls upon the metal mass which is pushed 


beneath it. But why does the falling hammer here exer- 
cise a greater force than when it is permitted simply to 
press with its own weight on the mass of metal ? Why is 
its power greater as the height from which it falls is 
increased, and the greater therefore the velocity of its 
fall ? We find, in fact, that the work performed by the 
hammer is determined by its velocity. In other cases, 
also, the velocity of moving masses is a means of pro- 
ducing great effects. I only remind you of the destruc- 
tive effects of musket-bullets, which in a state of rest are 
the most harmless things in the world. I remind you of 
the windmill, which derives its force from the moving 
air. It may appear surprising that motion, which we are 
accustomed to regard as a non-essential and transitory 
endowment of bodies, can produce such great effects. 
But the fact is, that motion appears to us, under ordinary 
circumstances, transitory, because the movement of all 
terrestrial bodies is resisted perpetually by other forces, 
friction, resistance of the air, &c., so that the motion is 
incessantly weakened and finally arrested. A body, how- 
ever, which is opposed by no resisting force, when once 
set in motion moves onward eternally with undiminished 
velocity. Thus we know that the planetary bodies have 
moved without change through space for thousands of 
years. Only by resisting forces can motion be diminished 
or destroyed. A moving body, such as the hammer or the 
musket-ball, when it strikes against another, presses 
the latter together, or penetrates it, until the sum of the 
resisting forces presented by the body struck to pres- 
sure, or to the separation of its particles, is sufficiently 
great to destroy the motion of the hammer or of the 
bullet. The motion of a mass regarded as taking the 
place of working force is called the living force (vis 
viva) of the mass. The word 6 living ' has of course here 
no reference whatever to living beings, but is intended to 


represent solely the force of the motion as distinguished 
from the state of unchanged rest from the gravity of a 
motionless body, for example, which produces an incessant 
pressure against the surface which supports it, but does 
not produce any motion. 

In the case before us, therefore, we had first power in 
the form of a falling mass of water, then in the form of 
a lifted hammer, and thirdly in the form of the living 
force of the falling hammer. We should transform the 
third form into the second, if we, for example, permitted 
the hammer to fall upon a highly elastic steel beam 
strong enough to resist the shock. The hammer would 
rebound, and in the most favourable case would reach a 
height equal to that from which it fell, but would never 
rise higher. In this way its mass would ascend ; and at 
the moment when its highest point has been attained it 
would represent the same number of raised foot-pounds 
as before it fell, never a greater number ; that is to say, 
living force can generate the same amount of work as 
that expended in its production. It is therefore equiva- 
lent to this quantity of work. 

Our clocks are driven by means of sinking weights, 
and our watches by means of the tension of springs. A 
weight which lies on the ground, an elastic spring which 
is without tension, can produce no effects : to obtain such 
we must first raise the weight or impart tension to the 
spring, which is accomplished when we wind up our 
clocks and watches. The man who winds the clock or 
watch communicates to the weight or to the spring a 
certain amount of power, and exactly so much as is thus 
communicated is gradually given out again during the 
following twenty-four hours, the original force being thus 
slowly consumed to overcome the friction of the wheels 
and the resistance which the pendulum encounters from 
the air. The wheelwork of the clock therefore developeg 


no working force, which was not previously communicated 
to it, but simply distributes the force given to it uniformly 
over a longer time. 

Into the chamber of an air-gun we squeeze, by means 
of a condensing air-pump, a great quantity of air. When 
we afterwards open the cock of the gun and admit the 
compressed air into the barrel, the ball is driven out of 
the latter with a force similar to that exerted by ignited 
powder. Now we may determine the work consumed in 
the pumping-in of the air, and the living force which, 
upon firing, is communicated to the ball, but we shall 
never find the latter greater than the former. The com- 
pressed air has generated no working force, but simply 
gives to the bullet that which has been previously com- 
municated to it. And while we have pumped for perhaps 
a quarter of an hour to charge the gun, the force is ex- 
pended in a few seconds when the bullet is discharged ; 
but because the action is compressed into so short a time, 
a much greater velocity is imparted to the ball than 
would be possible to communicate to it by the unaided 
effort of the arm in throwing it. 

From these examples you observe, and the mathe- 
matical theory has corroborated this for all purely 
mechanical, that is to say, for moving forces, that all our 
machinery and apparatus generate no force, but simply 
yield up the power communicated to them by natural 
forces, falling water, moving wind, or by the muscles of 
men and animals. After this law had been established 
by the great mathematicians of the last century, a per- 
petual motion, which should make use solely of pure 
mechanical forces, such as gravity, elasticity, pressure of 
liquids and gases, could only be sought after by be- 
wildered and ill-instructed people. But there are still 
other natural forces which are not reckoned among the 
purely moving forces, heat, electricity, magnetism, light, 


chemical forces, all of which nevertheless stand in mani- 
fold relation to mechanical processes. There is hardly a 
natural process to be found which is not accompanied by 
mechanical actions, or from which mechanical work may 
not be derived. Here the question of a perpetual motion 
remained open ; the decision of this question marks the 
progress of modern physics, regarding which I promised 
to address you. 

In the case of the air-gun, the work to be accomplished 
in the propulsion of the ball was given by the arm of the 
man who pumped in the air. In ordinary firearms, the 
condensed mass of air which propels the bullet is obtained 
in a totally different manner, namely, by the combustion 
of the powder. Gunpowder is transformed by combustion 
for the most part into gaseous products, which endeavour 
to occupy a much greater space than that previously 
taken up by the volume of the powder. Thus you see 
that, by the use of gunpowder, the work which the human 
arm must accomplish in the case of the air-gun is spared. 

In the mightiest of our machines, the steam-engine, it 
is a strongly compressed aeriform body, water vapour, 
which, by its effort to expand, sets the machine in motion. 
Here also we do not condense the steam by means of an 
external mechanical force, but by communicating heat to 
a mass of water in a closed boiler, we change this water 
into steam, which, in consequence of the limits of the 
space, is developed under strong pressure. In this case, 
therefore, it is the heat communicated which generates 
the mechanical force. The heat thus necessary for tiie 
machine we might obtain in many ways : the ordinary 
method is to procure it from the combustion of coal. 

Combustion is a chemical process. A particular con- 
stituent of our atmosphere, oxygen, possesses a strong 
force of attraction, or, as is said in chemistry, a strong 
affinity for the constituents of the combustible body, 


which affinity, however, in most cases can only exert 
itself at high temperatures. As soon as a portion of the 
combustible body, for example the coal, is sufficiently 
heated, the carbon unites itself with great violence to 
the oxygen of the atmosphere and forms a peculiar gas, 
carbonic acid, the same that we see foaming from beer 
and champagne. By this combination light and heat are 
generated ; heat is generally developed by any combina- 
tion of two bodies of strong affinity for each other ; and 
when the heat is intense enough, light appears. Hence 
in the steam-engine it is chemical processes and chemical 
forces which produce the astonishing work of these 
machines. In like manner the combustion of gunpowder 
is a chemical process, which in the barrel of the gun 
communicates living force to the bullet. 

While now the steam-engine developes for us mechanical 
work out of heat, we can conversely generate heat by me- 
chanical forces. Each impact, each act of friction does it. 
A skilful blacksmith can render an iron wedge red-hot by 
hammering. The axles of our carriages must be protected 
by careful greasing from ignition through friction. Even 
lately this property has been applied on a large scale. In 
some factories, where a surplus of water power is at hand, 
this surplus is applied to cause a strong iron plate to rotate 
rapidly upon another, so that they become strongly heated 
by the friction. The heat so obtained warms the room, and 
thus a stove without fuel is provided. Now could not 
the heat generated by the plates be applied to a small 
steam-engine, which in its turn should be able to keep 
the rubbing plates in motion? The perpetual motion 
would thus be at length found. This question might be 
asked, and could not be decided by the older mathematico- 
mechanical investigations. I will remark beforehand, 
that the general law which I will lay before you answers 
the question in the negative. 


By a similar plan, however, a speculative American set 
some time ago the industrial world of Europe in excite- 
ment. The magneto-electric machines often made use of 
in the case of rheumatic disorders are well known to the 
public. By imparting a swift rotation to the magnet of 
such a machine we obtain powerful currents of electricity. 
If those be conducted through water, the latter will be 
resolved into its two components, oxygen and hydrogen. 
By the combustion of hydrogen, water is again generated. 
If this combustion takes place, not in atmospheric air, of 
which oxygen only constitutes a fifth part, but in pure 
oxygen, and if a bit of chalk be placed in the flame, the 
chalk will be raised to its white heat, and give us the 
sun-like Drummond's light. At the same time the flame 
developes a considerable quantity of heat. Our American 
proposed to utilise in this way the gases obtained from 
electrolytic decomposition, and asserted, that by the com- 
bustion a sufficient amount of heat was generated to keep 
a small steam-engine in action, which again drove his 
magneto-electric machine, decomposed the water, and 
thus continually prepared its own fuel. This would cer- 
tainly have been the most splendid of all discoveries ; a 
perpetual motion which, besides the force that kept it 
going, generated light like the sun, and warmed all around 
it. The matter was by no means badly thought out. Each 
practical step in the aifair was known to be possible ; but 
those who at that time were acquainted with the phy- 
sical investigations which bear upon this subject, could 
have affirmed, on first hearing the report, that the matter 
was to be numbered among the numerous stories of the 
fable-rich America ; and indeed a fable it remained. 

It is not necessary to multiply examples further. You 
will infer from those given in what immediate connection 
heat, electricity, magnetism, light, and chemical affinity, 
stand with mechanical forces. 


Starting from each of these different manifestations of 
natural forces, we can set every other in motion, for the 
most part not in one way merely, but in many ways. It 
is here as with the weaver's web, 

Where a step stirs a thousand threads, 

The shuttles shoot from side to side, 

The fibres flow unseen, 

And one shock strikes a thousand combinations. 

Now it is clear that if by any means we could succeed, 
as the above American professed to have done, by me- 
chanical forces, in exciting chemical, electrical, or other 
natural processes, which, by any circuit whatever, and 
without altering permanently the active masses in the 
machine, could produce mechanical force in greater quan- 
tity than that at first applied, a portion of the work thus 
gained might be made use of to keep the machine in 
motion, while the rest of the work might be applied to 
any other purpose whatever. The problem was to find, 
in the complicated net of reciprocal actions, a track 
through chemical, electrical, magnetical, and thermic 
processes, back to mechanical actions, which might be 
followed with a final gain of mechanical work : thus would 
the perpetual motion be found. 

But, warned by the futility of former experiments, the 
public had become wiser. On the whole, people did not 
seek much after combinations which promised to furnish 
a perpetual motion, but the question was inverted. It 
was no more asked, How can I make use of the known 
and unknown relations of natural forces so as to construct 
a perpetual motion? but it was asked, If a perpetual 
motion be impossible, what are the relations which must 
subsist between natural forces ? Everything was gained 
by this inversion of the question. The relations of natural 
forces rendered necessary by the above assumption, might 


be easily and completely stated. It was found that all 
known relations of forces harmonise with the consequences 
of that assumption, and a series of unknown relations were 
discovered at the same time, the correctness of which re- 
mained to be proved. If a single one of them could be 
proved false, then a perpetual motion would be possible. 

The first who endeavoured to travel this way was a 
Frenchman named Carnot. in the year 1824. In spite of 
a too limited conception of his subject, and an incorrect 
view as to the nature of heat, which led him to some er- 
roneous conclusions, his experiment was not quite unsuc- 
cessful. He discovered a law which now bears his name, 
and to which I will return further on. 

His labours remained for a long time without notice, 
and it was not till eighteen years afterwards, that is in 

1842, that different investigators in different countries, 
and independent of Carnot, laid hold of the same thought. 
The first who saw truly the general law here referred to, 
and expressed it correctly, was a Grerman physician, J. R. 
Mayer of Heilbronn, in the year 1842. A little later, in 

1843, a Dane named Colding presented a memoir to the 
Academy of Copenhagen, in which the same law found 
utterance, and some experiments were described for its 
further corroboration. In England, Joule began about 
the same time to make experiments having reference to 
the same subject. We often find, in the case of questions 
to the solution of which the development of science 
points, that several heads, quite independent of each 
other, generate exactly the same series of reflections. 

I myself, without being acquainted with either Mayer 
or Colding, and having first made the acquaintance of 
Joule's experiments at the end of my investigation, fol- 
lowed the same path. I endeavoured to ascertain all the 
relations between the different natural processes, which 
followed from our regarding them from the above point of 


view. My inquiry was made public in 1847, in a small 
pamphlet bearing the title, ' On the Conservation of 
Force.' l 

Since that time the interest of the scientific public for 
this subject has gradually augmented, particularly in 
England, of which I had an opportunity of convincing 
myself during a visit last summer. A great number of 
the essential consequences of the above manner of view- 
ing the subject, the proof of which was wanting when the 
first theoretic notions were published, have since been 
confirmed by experiment, particularly by those of Joule ; 
and during the last year the most eminent physicist of 
France, Regnault, has adopted the. new mode of regarding 
the question, and by fresh investigations on the specific 
heat of gases has contributed much to its support. For 
some important consequences the experimental proof is 
still wanting, but the number of confirmations is so pre- 
dominant, that I have not deemed it premature to bring 
the subject before even a non-scientific audience. 

How the question has been decided you may already 
infer from, what has been stated. In the series of natural 
processes there is no circuit to be found, by which me- 
chanical force can be gained without a corresponding 
consumption. The perpetual motion remains impossible. 
Our reflections, however, gain thereby a higher interest. 

We have thus far regarded the development of force 
by natural processes, only in its relation to its usefulness 
to man, as mechanical force. You now see that we have 
arrived at a general law, which holds good wholly inde- 
pendent of the application which man makes of natural 
forces ; we must therefore make the expression of our law 
correspond to this more general significance. It is in the 
first place clear, that the work which, by any natural pro- 

1 There is a translation of this important Essay in the Scientific Memoirs^ 
New Series, p. 1H. J. T. 


cess whatever, is performed under favourable conditions 
by a machine, and which may be measured in the way 
already indicated, may be used as a measure of force com- 
mon to all. Further, the important question arises, If 
the quantity of force cannot be augmented except by 
corresponding consumption, can it be diminished or lost ? 
For the purposes of our machines it certainly can, if we 
neglect the opportunity to convert natural processes to use, 
but as investigation has proved, not for nature as a whole. 

In the collision and friction of bodies against each 
other, the mechanics of former years assumed simply that 
living force was lost. But I have already stated that each 
collision and each act of friction generates heat ; and, 
moreover, Joule has established by experiment the im- 
portant law, that for every foot-pound of force which is 
lost a definite quantity of heat is always generated, and 
that when work is performed by the consumption of heat, 
for each foot-pound thus gained a definite quantity of 
heat disappears. The quantity of heat necessary to raise 
the temperature of a pound of water a degree of the Cen- 
tigrade thermometer, corresponds to a mechanical force 
by which a pound weight would be raised to the height 
of 1,350 feet : we name this quantity the mechanical 
equivalent of heat. I may mention here that these facts 
conduct of necessity to the conclusion, that heat is not, as 
was formerly imagined, a fine imponderable substance, 
tut that, like light, it is a peculiar shivering motion of 
the ultimate particles of bodies. In collision and friction, 
according to this manner of viewing the subject, the mo- 
tion of the mass of a body which is apparently lost is con- 
verted into a motion of the ultimate particles of the 
body ; and conversely, when mechanical force is generated 
by heat, the motion of the ultimate particles is converted 
into a motion of the mass. 

Chemical combinations generate heat, and the quantity 


of this heat is totally independent of the time and steps 
through which the combination has been effected, pro- 
vided that other actions are not at the same time brought 
into play. If, however, mechanical work is at the same 
time accomplished, as in the case of the steam-engine, we 
obtain as much less heat as is equivalent to this work. 
The quantity of work produced by chemical force is in 
general very great. A pound of the purest coal gives, 
when burnt, sufficient heat to raise the temperature of 
8,086 pounds of water one degree of the Centigrade ther- 
mometer ; from this we can calculate that the magnitude 
of the chemical force of attraction between the particles 
of a pound of coal and the quantity of oxygen that cor- 
responds to it, is capable of lifting a weight of 100 pounds 
to a height of twenty miles. Unfortunately, in our steam- 
engines we have hitherto been able to gain only the 
smallest portion of this work, the greater part is lost in 
the shape of heat. The best expansive engines give back 
as mechanical work only 18 per cent, of the heat gene- 
rated by the fuel. 

From a similar investigation of all the other known 
physical and chemical processes, we arrive at the conclu- 
sion that Nature as a whole possesses a store of force 
which cannot in any way be either increased or dimi- 
nished, and that therefore the quantity of force in Nature 
is just as eternal and unalterable as the quantity of 
matter. Expressed in this form, I have named the general 
law ' The Principle of the Conservation of Force.' 

We cannot create mechanical force, but we may help 
ourselves from the general storehouse of Nature. The 
brook and the wind, which drive our mills, the forest and 
the coal-bed, which supply our steam-engines and warm 
our rooms, are to us the bearers of a small portion of the 
great natural supply which we draw upon for our pur- 
poses, and the actions of which we can apply as we think 


fit. The possessor of a mill claims the gravity of the 
descending rivulet, or the living force of the moving 
wind, as his possession. These portions of the store of 
Nature are what give his property its chief value. 

Further, from the fact that no portion of force can he 
absolutely lost, it does not follow that a portion may not 
be inapplicable to human purposes. In this respect the 
inferences drawn by William Thomson from the law of 
Carnot are of importance. This law, which was discovered 
by Carnot during his endeavours to ascertain the relations 
between heat and mechanical force, which, however, by 
no means belongs to the necessary consequences of the 
conservation of force, and which Clausius was the first to 
modify in such a manner that it no longer contradicted 
the above general law, expresses a certain relation between 
the compressibility, the capacity for heat, and the expan- 
sion by heat of all bodies. It is not yet completely proved 
in all directions, but some remarkable deductions having 
been drawn from it, and afterwards proved to be facts by 
experiment, it has attained thereby the highest degree of 
probability. Besides the mathematical form in which 
the law was first expressed by Carnot, we can give it the 
following more general expression : ' Only when heat 
passes from a warmer to a colder body, and even then 
only partially, can it be converted into mechanical work.' 

The heat of a body which we cannot cool further, 
cannot be changed into another form of force into 
electric or chemical force for example. Thus in our 
steam-engines we convert a portion of the heat of the 
glowing coal into work, by permitting it to pass to the 
less warm water of the boiler. If, however, all the bodies 
in Nature had the same temperature, it would be impos- 
sible to convert any portion of their heat into mechanical 
work. According to this we can divide the total force 
store of the universe into two parts, one of which is heat, 


and must continue to be such ; the other, to which a por- 
tion of the heat of the warmer bodies, and the total sup- 
ply of chemical, mechanical, electrical, and magnetical 
foraes belong, is capable of the most varied changes of 
f<>Tm, and constitutes the whole wealth of change which 
takes place in Nature. 

But the heat of the warmer bodies strives perpetually 
to pass to bodies less warm by radiation and conduction, 
and thus to establish an equilibrium of temperature. At 
each motion of a terrestrial body a portion of mechanical 
force passes by friction or collision into heat, of which 
only a part can be converted back again into mechanical 
force. This is also generally the case in every electrical 
and chemical process. From this it follows that the first 
portion of the store of force, the unchangeable heat, is 
augmented by every natural process, while the second 
portion, mechanical, electrical, and chemical force, must 
be diminished ; so that if the universe be delivered over 
to the undisturbed action of its physical processes, all 
force will finally pass into the form of heat, and all heat 
come into a state of equilibrium. Then all possibility of 
a further change would be at an end, and the complete 
cessation of all natural processes must set in. The life of 
men, animals, and plants could not of course continue if 
the sun had lost his high temperature, and with it his 
light, if all the components of the earth's surface had 
closed those combinations which their affinities demand. 
In short, the universe from that time forward would be 
condemned to a state of eternal rest. 

These consequences of the law of Carnot are, of course, 
only valid provided that the law, when sufficiently tested, 
proves to be universally correct. In the mean time there 
is little prospect of the law being proved incorrect. At 
all events, we must admire the sagacity of Thomson, who, 
in the letters of a long-known little mathematical for- 


mula, which only speaks of the heat, volume, and pressure 
of bodies, was able to discern consequences which threat- 
ened the universe, though certainly after an infinite period 
of time, with eternal death. 

I have already given you notice that our path lay 
through a thorny and unrefreshing field of mathematico- 
mechanical developments. We have now left this portion 
of our road behind us. The general principle which I 
have sought to lay before you has conducted us to a point 
from which our view is a wide one ; and aided by this 
principle, we can now at pleasure regard this or the other 
side of the surrounding world according as our interest 
in the matter leads us. A glance into the narrow labora- 
tory of the physicist, with its small appliances and com- 
plicated abstractions, will not be so attractive as a glance 
at the wide heaven above us, the clouds, the rivers, the 
woods, and the living beings around us. While regarding 
the laws which have been deduced from the physical 
processes of terrestrial bodies as applicable also to the 
heavenly bodies, let me remind you that the same force 
which, acting at the earth's surface, we call gravity 
(Schwere), acts as gravitation in the celestial spaces, and 
also manifests its power in the motion of the immeasu- 
rably distant double stars, which are governed by exactly 
the same laws as those subsisting between the earth and 
moon ; that therefore the light and heat of terrestrial 
bodies do not in any way differ essentially from those of 
the sun or of the most distant fixed star ; that the me- 
teoric stones which sometimes fall from external space 
upon the earth are composed of exactly the same simple 
chemical substances as those with which we are acquainted. 
We need, therefore, feel no scruple in granting that general 
laws to which all terrestrial natural processes are subject 
are also valid for other bodies than the earth. We will, 
therefore, make use of our law to glance over the house- 


hold of the universe with respect to the store of force, 
capable of action, which it possesses. 

A number of singular peculiarities in the structure of 
our planetary system indicate that it was once a connected 
mass, with a uniform motion of rotation. Without such 
an assumption it is impossible to explain why all the planets 
move in the same direction round the sun, why they all 
rotate in the same direction round their axes, why the 
planes of their orbits and those of their satellites and 
rings all nearly coincide, why all their orbits differ but 
little from circles, and much besides. From these re- 
maining indications of a former state astronomers have 
shaped an hypothesis regarding the formation of our 
planetary system, which, although from the nature of the 
case it must ever remain an hypothesis, still in its special 
traits is so well supported by analogy, that it certainly 
deserves our attention ; and the more so, as this notion 
in our own home, and within the walls of this town, 1 first 
found utterance. It was Kant who, feeling great interest 
in the physical description of the earth and the planetary 
system, undertook the labour of studying' the works of 
Newton ; and, as an evidence of the depth to which he 
had penetrated into the fundamental ideas of Newton, 
seized the notion that the same attractive force of all 
ponderable matter which now supports the motion of 
the planets must also aforetime have been able to form 
from matter loosely scattered in space the planetary 
system. Afterwards, and independent of Kant, Laplace, 
the great author of the c Mecanique celeste,' laid hold of 
the same thought, and introduced it among astronomers. 

The commencement of our planetary system, in- 
cluding the sun, must, according to this, be regarded 
as an immense nebulous mass which filled the portion 
of space now occupied by our system far beyond the 

1 Konigsberg. 


limits of Neptune, our most distant planet. Even now 
we discern in distant regions of the firmament nebulous 
patches the light of which, as spectrum analysis teaches, 
is the light of ignited gases ; and in their spectra we see 
more especially those bright lines which are produced by 
ignited hydrogen and by ignited nitrogen. Within our 
system, also, comets, the crowds of shooting stars, and the 
zodiacal light exhibit distinct traces of matter dispersed 
like powder, which moves, however, according to the law 
of gravitation, and is, at all events, partially retarded by 
the larger bodies and incorporated in them. The latter 
undoubtedly happens with the shooting stars and meteoric 
stones which come within the range of our atmosphere. 

If we calculate the density of the mass of our planetary 
system, according to the above assumption, for the time 
when it was a nebulous sphere, which reached to the path 
of the outermost planet, we should find that it would 
require several millions of cubic miles of such matter to 
weigh a single grain. 

The general attractive force of all matter must, how- 
ever, impel these masses to approach each other, and to 
condense, so that the nebulous sphere became incessantly 
smaller, by which, according to mechanical laws, a motion 
of rotation originally slow, and the existence of which 
must be assumed, would gradually become quicker and 
quicker. By the centrifugal force, which must act most 
energetically in the neighbourhood of the equator of the 
nebulous sphere, masses could from time to time be torn 
away, which afterwards would continue their courses 
separate from the main mass, forming themselves into 
single planets, or, similar to the great original sphere, 
into planets with satellites and rings, until finally the 
principal mass condensed itself into the sun. With 
regard to the origin of heat and light this theory origi- 
nally gave no information. 


When the nebulous chaos first separated itself from 
other fixed star masses it must not only have contained 
all kinds of matter which was to constitute the future 
planetary system, but also, in accordance with our new 
law, the whole store of force which at a future time ought 
to unfold therein its wealth of actions. Indeed, in this 
respect an immense dower was bestowed in the shape of 
the general attraction of all the particles for each other. 
This force, which on the earth exerts itself as gravity, 
acts in the heavenly spaces as gravitation. As terrestrial 
gravity when it draws a weight downwards performs work 
and generates vis viva, so also the heavenly bodies do the 
same when they draw two portions of matter from distant 
regions of space towards each other. 

The chemical forces must have been also present, ready 
to act ; but as these forces can only come into operation 
by the most intimate contact of the different masses, con- 
densation must have taken place before the play of chemical 
forces began. 

Whether a still further supply of force in the shape of 
heat was present at the commencement we do not know. 
At all events, by aid of the law of the equivalence of heat 
and work, we find in the mechanical forces existing at the 
time to which we refer such a rich source of heat and light, 
that there is no necessity whatever to take refuge in the 
idea of a store of these forces originally existing. When, 
through condensation of the masses, their particles came 
into collision and clung to each other, the vis viva of their 
motion would be thereby annihilated, and must reappear 
as heat. Already in old theories it has been calculated 
that cosmical masses must generate heat by their col- 
lision, but it was far from anybody's thought to make 
even a guess at the amount of heat to be generated in 
this way. At present we can give definite numerical- 
values with certainty. 


Let us make this addition to our assumption that, at 
the commencement, the density of the nebulous matter 
was a vanishing quantity as compared with the present 
density of the sun and planets : we can then calculate 
how much work has been performed by the condensation ; 
we can further calculate how much of this work still exists 
in the form of mechanical force, as attraction of the 
planets towards the sun, and as vis viva of their motion, 
and find by this how much of the force has been converted 
into heat. 

The result of this calculation 1 is, that only about the 
454th part of the original mechanical force remains as 
such, and that the remainder, converted into heat, would 
be sufficient to raise a mass of water equal to the sun and 
planets taken together, not less than twenty-eight millions 
of degrees of the Centigrade scale. For the sake of compa- 
rison, I will mention that the highest temperature which 
we can produce by the oxyhydrogen blowpipe, which is 
sufficient to fuse and vaporise even platinum, and which 
but few bodies can endure without melting, is estimated 
at about 2,000 degrees. Of the action of a temperature 
of twenty-eight millions of such degrees we can form no 
notion. If the mass of our entire system were pure coal, 
by the combustion of the whole of it only the 3,500th 
part of the above quantity would be generated. This 
is also clear, that such a great development of heat must 
have presented the greatest obstacle to the speedy union 
of the masses ; that the greater part of the heat must 
have been diffused by radiation into space, before the 
masses could form bodies possessing the present density 
of the sun and planets, and that these bodies must once 
have been in a state of fiery fluidity. This notion is cor- 
roborated by the geological phenomena of our planet ; 
and with regard to the other planetary bodies, the flat- 
1 See note on page 193. 


tened form of the sphere, which is the form of equili- 
brium of a fluid mass, is indicative of a former state of 
fluidity. If I thus permit an immense quantity of heafc 
to disappear without compensation from our system, the 
principle of the conservation of force is not thereby in- 
vaded. Certainly for our planet it is lost, but not for the 
universe. It has proceeded outwards, and daily proceeds 
outwards into infinite space ; and we know not whether 
the medium which transmits the undulations of light 
and heat possesses an end where the rays must return, or 
whether they eternally pursue their way through infinitude. 

The store of force at present possessed by our system is 
also equivalent to immense quantities of heat. If our 
earth were by a sudden shock brought to rest in her orbit 
which is not to be feared in the existing arrangement 
of our system by such a shock a quantity of heat would 
be generated equal to that produced by the combustion of 
fourteen such earths of solid coal. Making the most un- 
favourable assumption as to its capacity for heat that 
is, placing it equal to that of water the mass of the earth 
would thereby be heated 11,200 degrees ; it would, there- 
fore, be quite fused, and for the most part converted into 
vapour. If, then, the earth, after having been thus 
brought to rest, should fall into the sun which, of 
course, would be the case the quantity of heat deve- 
loped by the shock would be 400 times greater. 

Even now from time to time such a process is repeated 
on a small scale. There can hardly be a doubt that 
meteors, fireballs, and meteoric stones are masses which 
belong to the universe, and before coming into the 
domain of our earth, moved like the planets round the 
sun. Only when they enter our atmosphere do they 
become visible and fa-11 sometimes to the earth. In order 
to explain the emission of light by these bodies, and the 
fact that for some time after their descent they are very 


hot, the friction was long ago thought of which they 
experience in passing through the air. We can now 
calculate that a velocity of 3,000 feet a second, supposing 
the whole of the friction to be expended in heating the 
solid mass, would raise a piece of meteoric iron 1,000 C. 
in temperature, or, in other words, to a vivid red heat. 
Now the average velocity of the meteors seems to be 
thirty to fifty times the above amount. To compensate 
this, however, the greater portion of the heat is doubtless 
carried away by the condensed mass of air which the 
meteor drives before it. It is known that bright meteors- 
generally leave a luminous trail behind them, which 
probably consists of severed portions of the red-hot sur- 
faces. Meteoric masses which fall to the earth often 
burst with a violent explosion, which may be regarded as 
a result of the quick heating. The newly-fallen pieces 
have been for the most part found hot, but not red-hot, 
which is easily explainable by the circumstance, that 
during the short time occupied by the meteor in passing 
through the atmosphere, only a thin superficial layer is 
heated to redness, while but a small quantity of heat has 
been able to penetrate to the interior of the mass. For 
this reason the red heat can speedily disappear, 

Thus has the falling of the meteoric stone, the minute 
remnant of processes which seem to have played an im- 
portant part in the formation of the heavenly bodies, 
conducted us to the present time, where we pass from 
the darkness of hypothetical views to the brightness of 
knowledge. In what we have said, however, all that is 
hypothetical is the assumption of Kant and Laplace, 
that the masses of our system were once distributed as 
nebulae in space. 

On account of the rarity of the case, we will still 
further remark in what close coincidence the results of 
science here stand with the earlier legends of the human 


family, and the forebodings of poetic fancy. The cos- 
mogony of ancient nations generally commences with 
chaos and darkness. Thus for example Mephistopheles 

says : 

Part of the Part am I, once All, in primal night, 
Part of the Darkness which brought forth the Light, 
The haughty Light, which now disputes the space, 
And claims of Mother Night her ancient place. 

Neither is the Mosaic tradition very divergent, par- 
ticularly when we remember that that which Moses 
names heaven, is different from the blue dome above us, 
and is synonymous with space, and that the unformed 
earth and the waters of the great deep, which were 
afterwards divided into waters above the firmament and 
waters below the firmament, resembled the chaotic com- 
ponents of the world : 

'In the beginning God created the heaven and the earth. 

' And the earth was without form, and void ; and dark- 
ness was upon the face of the deep. And the spirit of 
God moved upon the face of the waters.' 

And just as in nebulous sphere, just become luminous, 
and in the new red-hot liquid earth of our modern cosmo- 
gony light was not yet divided into sun and stars, nor time 
into day and night, as it was after the earth had cooled. 

6 And God divided the light from the darkness. 

( And God called the light day, and the darkness He 
called night. And the evening and the morning were 
the first day.' 

And now, first, after the waters had been gathered 
together into the sea, and the earth had been laid dry, 
could plants and animals be formed. 

Our earth bears still the unmistakeable traces of its 
old fiery fluid condition. The granite formations of her 
xaountains exhibit a structure, which can only be pro- 


duced by the crystallisation of fused masses. Investiga- 
tion still shows that the temperature in mines and 
borings increases as we descend ; and if this increase is 
uniform, at the depth of fifty miles a heat exists sufficient 
to fuse all our minerals. Even now our volcanoes pro- 
ject from time to time mighty masses of fused rocks from 
their interior, as a testimony of the heat which exists 
there. But the cooled crust of the earth has already 
become so thick, that, as may be shown by calculations of 
its conductive power, the heat coming to the surface 
from within, in comparison with that reaching the earth 
from the sun, is exceedingly small, and increases the 
temperature of the surface only about ^th of a degree 
Centigrade ; so that the remnant of the old store of force 
which is enclosed as heat within the bowels of the earth 
has a sensible influence upon the processes at the earth's 
surface only through the instrumentality of volcanic 
phsenomena. Those processes owe their power almost 
wholly to the action of other heavenly bodies, particu- 
larly to the light and heat of the sun, and partly also, in 
the case of the tides, to the attraction of the sun and moon. 
Most varied and numerous are the changes which we 
owe to the light and heat of the sun. The sun heats our 
atmosphere irregularly, the warm rarefied air ascends, 
while fresh cool air flows from the sides to supply its 
place : in this way winds are generated. This action is 
most powerful at the equator, the warm air of which 
incessantly flows in the upper regions of the atmosphere 
towards the poles ; while just as persistently at the 
earth's surface, the trade-wind carries new and cool air 
to the equator. Without the heat of the sun, all winds 
must of necessity cease. Similar currents are produced 
by the same cause in the waters of the sea. Their 
power may be inferred from the influence which in some 
cases they exert upon climate. By them the warn) 


water of the Antilles is carried to the British Isles, and 
confers upon them a mild uniform warmth, and rich 
moisture ; while, through similar causes, the floating ice 
of the North Pole is carried to the coast of Newfoundland 
and produces raw cold. Further, by- the heat of the sun 
a portion of the water is converted into vapour, which 
rises in the atmosphere, is condensed to clouds, or falls 
in rain and snow upon the earth, collects in the form of 
springs, brooks, and rivers, and finally reaches the sea 
again, after having gnawed the rocks, carried away light 
earth, and thus performed its part in the geologic 
changes of the earth ; perhaps besides all this it has 
driven our water-mill upon its way. If the heat of the 
sun were withdrawn, there would remain only a single 
motion of water, namely, the tides, which are produced 
by the attraction of the sun and moon. 

How is it, now, with the motions and the work of 
organic beings ? To the builders of the automata of the 
last century, men and animals appeared as clockwork 
which was never wound up, and created the force which 
they exerted out of nothing. They did not know how 
to establish a connexion between the nutriment con- 
sumed and the work generated. Since, however, we 
have learned to discern in the steam-engine this origin 
of mechanical force, we must inquire whether something 
similar does not hold good with regard to men. Indeed, 
the continuation of life is dependent on the consumption 
of nutritive materials : these are combustible substances, 
which, after digestion and being passed into the blood, 
actually undergo a slow combustion, and finally enter 
into almost the same combinations with the oxygen of 
the atmosphere that are produced in an open fire. As 
the quantity of heat generated by combustion is inde- 
pendent of the duration of the combustion and the steps 
in which it occurs, we can calculate from the mass of the 


consumed material how much heafc, or its equivalent 
work, is thereby generated in an animal body. Unfor- 
tunately, the difficulty of the experiments is still very 
great ; but within those limits of accuracy which have 
been as yet attainable, the experiments show that the 
heat generated in the animal body corresponds to the 
amount which would be generated by the chemical pro- 
cesses. The animal body therefore does not differ from 
the steam-engine as regards the manner in which it 
obtains heat and force, but does differ from it in the 
manner in which the force gained is to be made use of. 
The body is, besides, more limited than the machine in 
the choice of its fuel ; the latter could be heated with 
sugar, with starch-flour, and butter, just as well as with 
coal or wood ; the animal body must dissolve its mate- 
rials artificially, and distribute them through its system ; 
it must, further, perpetually renew the used-up materials 
of its organs, and as it cannot itself create the matter 
necessary for this, the matter must come from without. 
Liebig was the first to point out these various uses of 
the consumed nutriment. As material for the perpetual 
renewal of the body, it seems that certain definite albu- 
minous substances which appear in plants, and form the 
chief mass of the animal body, can alone be used. They 
form only a portion of the mass of nutriment taken 
daily ; the remainder, sugar, starch, fat, are really only 
materials for warming, and are perhaps not to be super- 
seded by coal, simply because the latter does not permit 
itself to be dissolved. 

If, then, the processes in the animal body are not in 
this respect to be distinguished from inorganic processes, 
the question arises, whence comes the nutriment which 
constitutes the source of the body's force ? The answer 
is, from the vegetable kingdom ; for only the material 
of plants, or the flesh of herbivorous animals, can be 


made use of for food. The animals which live on plants 
occupy a mean position between carnivorous animals, in 
which we reckon man, and vegetables, which the former 
could not make use of immediately as nutriment. In 
hay and grass the same nutritive substances are present 
as in meal and flour, bat in less quantity. As, however, 
the digestive organs of man are not in a condition to 
extract the small quantity of the useful from the great 
excess of the insoluble, we submit, in the first place, 
these substances to the powerful digestion of the ox, 
permit the nourishment to store itself in the animal's 
body, in order in the end to gain it for ourselves in a more 
agreeable and useful form. In answer to our question, 
therefore, we are referred to the vegetable world. Now 
when what plants take in and what they give out are 
made the subjects of investigation, we find that the 
principal part of the former consists in the products of 
combustion which are generated by the animal. They 
take the consumed carbon given off in respiration, as 
carbonic acid, from the air, the consumed hydrogen as 
water, the nitrogen in its simplest and closest com- 
bination as ammonia ; and from these materials, with the 
assistance of small ingredients which they take from the 
soil, they generate anew the compound combustible sub- 
stances, albumen, sugar, oil, on which the animal subsists. 
Here, therefore, is a circuit which appears to be a per- 
petual store of force. Plants prepare fuel and nutri- 
ment, animals consume these, burn them slowly in their 
lungs, and from the products of combustion the plants 
again derive their nutriment. The latter is an eternal 
source of chemical, the former of mechanical forces. 
Would not the combination of both organic kingdoms 
produce the perpetual motion ? We must not conclude 
hastily : further inquiry shows, that plants are capable of 
producing combustible substances only when they are 


under the influence of the sun. A portion of the sun's 
rays exhibits a remarkable relation to chemical forces, it 
can produce and destroy chemical combinations ; and these 
rays, which for the most part are blue or violet, are called 
therefore chemical rays. We make use of their action in 
the production of photographs. Here compounds of silver 
are decomposed at the place where the sun's rays strike 
them. The same rays overpower in the green leaves of 
plants the strong chemical affinity of the carbon of the 
carbonic acid for oxygen, give back the latter free to the 
atmosphere, and accumulate the other, in combination 
with other bodies, as woody fibre, starch, oil, or resin. 
These chemically active rays of the sun disappear com- 
pletely as soon as they encounter the green portions of 
the plants, and hence it is that in Daguerreotype images 
the green leaves of plants appear uniformly black. In- 
asmuch as the light coming from them does not contain 
the chemical rays, it is unable to act upon the silver 
compounds. But besides the blue and violet, the yellow 
rays play an important part in. the growth of plants. 
They also are comparatively strongly absorbed by the 

Hence a certain portion of force disappears from the 
sunlight, while combustible substances are generated and 
accumulated in plants ; and we can assume it as very 
probable, that the former is the cause of the latter. I 
must indeed remark, that we are in possession of no ex- 
periments from which we might determine whether the 
vis viva of the sun's rays which have disappeared corre- 
sponds to the chemical forces accumulated during the 
same time ; and as long as these experiments are wanting, 
we cannot regard the stated relation as a certainty. If 
this view should prove correct, we derive from it the 
flattering result, that all force, by means of which our 
bodies live and move, finds its source in the purest sun- 


light ; and hence we are all, in point of nobility, not 
behind the race of the great monarch of China, who 
heretofore alone called himself Son of the Sun. But it 
must also be conceded, that our lower fellow-beings, the 
frog and leech, share the same sethereal origin, as also the 
whole vegetable world, and even the fuel which comes to 
us from the ages past, as well as the youngest offspring 
of the forest with which we heat our stoves and set our 
machines in motion. 

You see, then, that the immense wealth of ever- 
changing meteorological, climatic, geological, and organic 
processes of our earth are almost wholly preserved in 
action by the light- and heat-giving rays of the sun ; and 
you see in this a remarkable example, how Proteus-like 
the effects of a single cause, under altered external con- 
ditions, may exhibit itself in nature. Besides these, the 
earth experiences an action of another kind from its 
central luminary, as well as from its satellite the moon, 
which exhibits itself in the remarkable phenomenon of 
the ebb and flow of the tide. 

Each of these bodies excites, by its attraction upon the 
waters of the sea, two gigantic waves, which flow in the 
same direction round the world, as the attracting bodies 
themselves apparently do. The two waves of the moon, 
on account of her greater nearness, are about 3J times 
as large as those excited by the sun. One of these waves 
has its crest on the quarter of the earth's surface which is 
turned towards the moon, the other is at the opposite 
side. Both these quarters possess the flow of the tide, 
while the regions which lie between have the ebb. Al- 
though in the open sea the height of the tide amounts to 
only about three feet, and only in certain narrow channels, 
where the moving water is squeezed together, rises to 
thirty feet, the might of the phenomenon is nevertheless 
manifest from the calculation of Bessel, according to 


which a quarter of the earth covered by the sea possesses, 
during the flow of the tide, about 22,000 cubic miles of 
water more than during the ebb, and that therefore such 
a mass of water must, in 6 hours, flow from one quarter 
of the earth to the other. 

The phenomenon of the ebb and flow, as already recog- 
nised by Mayer, combined with the law of the conserva- 
tion of force, stands in remarkable connexion with the 
question of the stability of our planetary system. The 
mechanical theory of the planetary motions discovered 
by Newton teaches, that if a solid body in absolute vacua, 
attracted by the sun, move around him in the same 
manner as the" planets, this motion will endure unchanged 
through all eternity. 

Now we have actually not only one, but several such 
planets, which move around the sun, and by their mutual 
attraction create little changes and disturbances in each 
other's paths. Nevertheless Laplace, in his great work, 
the ' Mecanique celeste,' has proved that in our planetary 
system all these disturbances increase and diminish peri- 
odically, and can never exceed certain limits, so that by 
this cause the eternal existence of the planetary system is 

But I have already named two assumptions which must 
be made : first, that the celestial spaces must be abso- 
lutely empty ; and secondly, that the sun and planets 
must be solid bodies. The first is at least the case as 
far as astronomical observations reach, for they have 
never been able to detect any retardation of the planets, 
such as would occur if they moved in a resisting medium. 
But on a body of less mass, the comet of Encke, changes 
are observed of such a nature : this comet describes 
ellipses round the sun which are becoming gradually 
smaller. If this kind of motion, which certainly corre- 
sponds to that through a resisting medium, be actually 


due to the existence of such a medium, a time will come 
when the comet will strike the sun ; and a similar end 
threatens all the planets, although after a time, the 
length of which baffles our imagination to conceive of it. 
But even should the existence of a resisting medium 
appear doubtful to us, there is no doubt that the planets 
are not wholly composed of solid materials which are 
inseparably bound together. Signs of the existence of an 
atmosphere are observed on the Sun, on Venus, Mars, 
Jupiter, and Saturn. Signs of water and ice upon Mars ; 
and our earth has undoubtedly a fluid portion on its 
surface, and perhaps a still greater portion of fluid within 
it. The motions of the tides, however, produce friction, 
all friction destroys vis viva, and the loss in this case can 
only affect the vis viva of the planetary system. We 
come thereby to the unavoidable conclusion, that every 
tide, although with infinite slowness, still with certainty 
diminishes the store of mechanical force of the system ; 
and as a consequence of this, the rotation of the planets 
in question round their axes must become more slow. 
The recent careful investigations of the moon's motion 
made by Hansen, Adams, and Delaunay, have proved that 
the earth does experience such a retardation. According 
to the former, the length of each sidereal day has in- 
creased since the time of Hipparchus by the -^ part of a 
second, and the duration of a century by half a quarter 
of an hour ; according to Adams and Sir W. Thomson, 
the increase has been almost twice as great. A clock 
which went right at the beginning of a century, would 
be twenty-two seconds in advance of the earth at the end 
of the century. Laplace had denied the existence of 
such a retardation in the case of the earth ; to ascertain 
the amount, the theory of lunar motion required a greater 
development than was possible in his time. The final 
consequence would be, but after millions of years, if in 


the mean time tLe ocean did not become frozen, that one 
side of the earth would be constantly turned towards the 
sun, and enjoy a perpetual day, whereas the opposite side 
would be involved in eternal night. Such a position we 
observe in our moon with regard to the earth, and also in 
the case of the satellites as regards their planets ; it is, 
perhaps, due to the action of the mighty ebb and flow to 
which these bodies, in the time of their fiery fluid con- 
dition, were subjected. 

I would not have brought forward these conclusions, 
which again plunge us in the most distant future, if they 
were not unavoidable. Physico-mechanical laws are, as 
it were, the telescopes of our spiritual eye, which can 
penetrate into the deepest night of time, past and to 

Another essential question as regards the future of our 
planetary system has reference to its future temperature 
and illumination. As the internal heat of the earth has 
but little influence on the temperature of the surface, 
the heat of the sun is the only thing which essentially 
affects the question. The quantity of heat falling from 
the sun during a given time upon a given portion of the 
earth's surface may be measured, and from this it can be 
calculated how much heat in a given time is sent out 
from the entire sun. Such measurements have been 
made by the French physicist Pouillet, and it has been 
found that the sun gives out a quantity of heat per hour 
equal to that which a layer of the densest coal 10 feet 
thick would give out by its combustion ; and hence in a 
year a quantity equal to the combustion of a layer of 
17 miles. If this heat were drawn uniformly from the 
entire mass of the sun, its temperature would only be 
diminished thereby 1J of a degree Centigrade per year, 
assuming its capacity for heat to be equal to that of water. 
These results can give us an idea of the magnitude of the 


emission, in relation to the surface and mass of the sun ; 
but they cannot inform us whether the sun radiates 
heat as a glowing body, which since its formation has its 
heat accumulated within it, or whether a new generation 
of heat by chemical processes is continually taking place 
at the sun's surface. At all events, the law of the con- 
servation of force teaches us that no process analogous to 
those known at the surface of the earth can supply for 
eternity an inexhaustible amount of light and heat to 
the sun. But the same law also teaches that the store of 
force at present existing, as heat, or as what may become 
heat, is sufficient for an immeasurable time. With re- 
gard to the store of chemical force in the sun, we can 
form no conjecture, and the store of heat there existing 
can only be determined by very uncertain estimations. 
If, however, we adopt the very probable view, that the 
remarkably small density of so large a body is caused by 
its high temperature, and may become greater in time, it 
may be calculated that if the diameter of the sun were 
diminished only the ten-thousandth part of its present 
length, by this act a sufficient quantity of heat would be 
generated to cover the total emission for 2,100 years. 
So small a change it would be difficult to detect even by 
the finest astronomical observations. 

Indeed, from the commencement of the period during 
which we possess historic accounts, that is, for a period of 
about 4,000 years, the temperature of the earth has not 
sensibly diminished. From these old ages we have cer- 
tainly no thermometric observations, but we have infor- 
mation regarding the distribution of certain cultivated 
plants, the vine, the olive tree, which are very sensitive 
to changes of the mean annual temperature, and we find 
that these plants at the present moment have the same 
limits of distribution that they had in the times of 
Abraham and Homer ; from which we may infer back- 
wards the constancy of the climate. 


In opposition to this it has been urged, that here in 
Prussia the German knights in former times cultivated 
the vine, cellared their own wine and drank it, which is 
no longer possible. From this the conclusion has been 
drawn, that the heat of our climate has diminished since 
the time referred to. Against this, however, Dove lias 
cited the reports of ancient chroniclers, according to 
which, in some peculiarly hot years, the Prussian grape 
possessed somewhat less than its usual quantity of acid. 
The fact also speaks not so much for the climate of the 
country as for the throats of the German drinkers. 

But even though the force store of our planetary 
system is so immensely great, that by the incessant 
emission which has occurred during the period of human 
history it has not been sensibly diminished, even though 
the length of the time which must flow by before a sen- 
sible change in the state of our planetary system occurs 
is totally incapable of measurement; still the inexorable 
laws of mechanics indicate that this store of force, which 
can only suffer loss and not gain, must be finally exhausted. 
Shall we terrify ourselves by this thought ? Men are in 
the habit of measuring the greatness and the wisdom of 
the universe by the duration and the profit which it pro- 
mises to their own race ; but the past history of the earth 
already shows what an insignificant moment tha duration 
of the existence of our race upon it constitutes. A 
Nineveh vessel, a Eoman sword, awake in us the con- 
ception of grey antiquity. What the museums of Europe 
show us of the remains of Egypt and Assyria we gaze 
upon with silent astonishment, and despair of being able 
to carry our thoughts back to a period so remote. Still 
must the human race have existed for ages, and multi- 
plied itself before the Pyramids or Nineveh could have 
been erected. We estimate the duration of human his- 
tory at 6,000 years ; but immeasurable as this time may 


appear to us, what is it in comparison with the time 
during which the earth carried successive series of rank 
plants and mighty animals, and no men ; during which in 
our neighbourhood the amber- tree bloomed, and dropped 
its costly gum on the earth and in the sea ; when in Sibe- 
ria, Europe, and North America groves of tropical palms 
nourished ; where gigantic lizards, and after them ele- 
phants, whose mighty remains we still find buried in 
the earth, found a home? Different geologists, pro- 
ceeding from different premises, have sought to esti- 
mate the duration of the above-named creative period, 
and vary from a million to nine million years. The 
time during which the earth generated organic beings 
is again small when compared with the ages during 
which the world was a ball of fused rocks. For the 
duration of its cooling from 2,000 to 200 Centigrade 
the experiments of Bishop upon basalt show that about 
350 millions of years would be necessary. And with re- 
gard to the time during which the first nebulous mass 
condensed into our planetary system, our most daring 
conjectures must cease. The history of man, therefore, 
is but a short ripple in the ocean of time. For a much 
longer series of years than that during which he has 
already occupied this world, the existence of the present 
state of inorganic nature favourable to the duration of 
man seems to be secured, so that for ourselves and for 
long generations after us we have nothing to fear. But 
the same forces of air and water, and of the volcanic 
interior, which produced former geological revolutions, 
and buried one series of living forms after another, act 
still upon the earth's crust. They more probably will 
bring about the last day of the human race than those 
distant cosmical alterations of which we have spoken, 
forcing us perhaps to make way for new and more com- 
plete living forms, as the lizards and the mammoth 


Lave given place to us and our fellow-creatures which 
now exist. 

Thus the thread which was spun in darkness by those 
who sought a perpetual motion has conducted us to a uni- 
versal law of nature, which radiates light into the distant 
nights of the beginning and of the end of the history of 
the universe. To our own race it permits a long but not 
an endless existence ; it threatens it with a day of judg- 
ment, the dawn of which is still happily obscured. As 
each of us singly must endure the thought of his death, 
the race must endure the same. But above the forms of 
life gone by, the human race has higher moral problems 
before it, the bearer of which it is, and in the completion 
of which it fulfils its destiny. 



I must here explain the calculation of the heat which 
must be produced by the assumed condensation of the 
bodies of our system from scattered nebulous matter. 
The other calculations, the results of which I have men- 
tioned, are to be found partly in J. E. Mayer's papers, 
partly in Joule's communications, and partly by aid of 
the known facts and method of science : they are easily 

The measure of the work performed by the condensation 
of the mass from a state of infinitely small density is the 
potential of the condensed mass upon itself. For a sphere 
of uniform density of the mass M, and the radius K, the 
potential upon itself V if we call the mass of the earth 
772, its radius r, and the intensity of gravity at its 
surface g has the value 


Let us regard the bodies of our system as such spheres, 
then the total work of condensation is equal to the sum 
of all their potentials on themselves. As, however, these 
potentials for different spheres are to each other as the 

M 2 

quantity , they all vanish in comparison with the sun ; 

even that of the greatest planet, Jupiter, is only about the 
one hundred-thousandth part of that of the sun ; in the 
calculation, therefore, it is only necessary to introduce the 

To elevate the temperature of a mass M of the specific 
heat <7, t degrees, we need a quantity of heat equal to 


Mat ; this corresponds, when Kg represents the mechanical 
equivalent of the unit of heat, to the work A^Motf. To 
find the elevation of temperature produced by the con- 
densation of the mass of the sun, let us set 

we have then 

3 rM 

~5 A.K. m. a 

For a mass of water equal to the sun we have <r = 1 ; 
then the calculation with the known values of A, M, R, ?w, 
and r, gives 

t = 2861 1000 Cent. 

The mass of the sun is 738 times greater than that of 
all the planets taken together ; if, therefore, we desire to 
make the water mass equal to that of the entire system, 

we must multiply the value of t by the fraction , which 

makes hardly a sensible alteration in the result. 

When a spherical mass of the radius R condenses more 
and more to the radius R p the elevation of temperature 
thereby produced is 

SA.wwlR, R 


_3. r 2 M 


Supposing, then ; the mass of the planetary system to be 
at the commencement, not a sphere of infinite radius, but 
limited, say of the radius of the path of Neptune, which 
is six thousand times greater than the radius of the sun, 

the magnitude 1 will then be equal to 600 o, and the above 


value of t would have to be diminished by this inconsi- 
derable amount. 


From the same formula we can deduce that a diminution 
of joj^j of the radius of the sun would generate work in a 
water mass equal to the sun, equivalent to 2,861 degrees 
Centigrade. And as, according to Pouillet, a quantity of 
heat corresponding to 1 J degree is lost annually in such a 
mass, the condensation referred to would cover the loss for 
2,289 years. 

If the sun, as seems probable, be not everywhere of the 
same density, but is denser at the centre than near the 
surface, the potential of its mass and the corresponding 
quantity of heat will be still greater. 

Of the now remaining mechanical forces, the vis viva of 
the rotation of the heavenly bodies round their own axes 
is, in comparison with the other quantities, very small, 
and may be neglected. The vis viva of the motion of 
revolution round the sun, if //, be the mass of a planet, 
and p its distance from the sun, is 

m 2p 

Omitting the quantity as very small compared with - , 
2p K 

and dividing by the above value of V, we obtain 

L 5 ft 
V = 3 M* 

The mass of all the planets together is ,- of the mass 


of the sun ; hence the value of L for the entire system is 




THE physiology of the senses is a border land in which 
the two great divisions of human knowledge, natural and 
mental science, encroach on one another's domain ; in 
which problems arise which are important for both, and 
which only the combined labour of both can solve. 

No doubt the first concern of physiology is only with 
material changes in material organs, and that of the 
special physiology of the senses is with the nerves and 
their sensations, so far as these are excitations of the 
nerves. But, in the course of investigation into the 
functions of the organs of the senses, science cannot avoid 
also considering the apprehension of external objects, 
which is the result of these excitations of the nerves, 
and for the simple reason that the fact of a particular 
state of mental apprehension often reveals to us a nervous 
excitation which would otherwise have escaped our notice. 
On the other hand, apprehension of external objects must 
always be an act of our power of realization, and must 
therefore be accompanied by consciousness, for it is a 
mental function. Indeed the further exact investigation 
of this process has been pushed, the more it has revealed 
to us an ever-widening field of such mental functions. 


the results of which are involved in those acts of appre- 
hension by the senses which at first sight appear to be 
most simple and immediate. These concealed functions 
have been but little discussed, because we are so ac- 
customed to regard the apprehension of any external 
object as a complete and direct whole, which does not 
admit of analysis. 

It is scarcely necessary for me to remind my present 
readers of the fundamental importance of this field of 
inquiry to almost every other department of science. 
For apprehension by the senses supplies after all, directly 
or indirectly, the material of all human knowledge, or 
at least the stimulus necessary to develope every inborn 
faculty of the mind. It supplies the basis for the whole 
action of man upon the outer world ; and if this stage of 
mental processes is admitted to be the simplest and lowest 
of its kind, it is none the less important and interesting. 
For there is little hope that he who does not begin at 
the beginning of knowledge will ever arrive at its end. 

It is by this path that the art of experiment, which 
has become so important in natural science, found en- 
trance into the hitherto inaccessible field of mental 
processes. At first this will be only so far as we are 
able by experiment to determine the particular sensible 
impressions which call up one or another conception 
in our consciousness. But from this first step will follow 
numerous deductions as to the nature of the mental 
processes which contribute to the result. I will therefore 
endeavour to give some account of the results of physi- 
ological inquiries so far as they bear on the questions 
above mentioned. 

I am the more desirous of doing so because I have 
lately completed ] a complete survey of the field of physio- 
logical optics, and am happy to have an opportunity of 

1 Prof. Helmholtz's Handbook of Physiological Optics was published at 
Leipzig in 1867. 


putting together in a compendious form the views and 
deductions on the present subject which might escape 
notice among the numerous details of a book devoted to 


the special objects of natural science. I may state that 
in that work I took great pains to convince myself of 
the truth of every fact of the slightest importance by 
personal observation and experiment. There is no longer 
much controversy on the more important facts of obser- 
vation, the chief difference of opinion being as to the 
extent of certain individual differences of apprehension 
by the senses. During the last few years a great number 
of distinguished investigators have, under the influence 
of the rapid progress of ophthalmic medicine, worked at 
the physiology of vision ; and in proportion as the 
number of observed facts has increased, they have 
also become more capable of scientific arrangement and 
explanation. I need not remind those of my readers 
who are conversant with the subject how much labour 
must be expended to establish many facts which appeal- 
comparatively simple and almost self-evident. 

To render what follows understood in all its bearings, 
I shall first describe the physical characters of the eye 
as an optical instrument ; next the physiological pro- 
cesses of excitation and conduction in the parts of the 
nervous system which belong to it ; and lastly I shall 
take up the psychological question, how mental appre- 
hensions are produced by the changes which take place in 
the optic nerve. 

The first part of our inquiry, which cannot be passed 
over because it is the foundation of what follows, will 
be in great part a repetition of what is already generally 
known, in order to bring in what is new in its proper 
place. But it is just this part of the subject which 
excites so much interest, as the real starting point of 


that remarkable progress which ophthalmic medicine has 
made during the last twenty years a progress which 
for its rapidity and scientific character is perhaps without 
parallel in the history of the healing art. 

Every lover of his kind must rejoice in these achieve- 
ments which ward off or remove so much misery that 
formerly we were powerless to help, but a man of science 
has peculiar reason to look on them with pride. For 
this wonderful advance has not been achieved by groping 
and lucky finding, but by deduction rigidly followed out, 
and thus carries with it the pledge of still future suc- 
cesses. As once astronomy was the pattern from which 
the other sciences learned how the right method will 
lead to success, so does ophthalmic medicine now dis- 
play how much may be accomplished in the treatment 
of disease by extended application of well-understood 
methods of investigation and accurate insight into the 
causal connection of phenomena. It is no wonder that 
the right sort of men were drawn to an arena which 
offered a prospect of new and noble victories over the 
opposing powers of nature to the true scientific spirit 
the spirit of patient and cheerful work. It was because 
there were so many of them that the success was so 
brilliant. Let me be permitted to name out of the 
whole number a representative of each of the three 
nations of common origin which have contributed most 
to the result : Yon Graefe in Germany, Bonders in 
Holland, and Bowman in England. 

There is another point of view from which this advance 
in ophthalmology may be regarded, and that with equal 
satisfaction. Schiller says of science: 

Wer um die Gottin freit, suche in ihr nicht das Weib. 1 
Wlio woos the goddess must not hope the wife. 

1 From Schiller's Spruche. Literally, ' Let not him who socks the lot e 
of a goddess expect to find in her the woman.' 


And history teaches us, what we shall have opportunity 
of seeing in the present inquiry, that the most important 
practical results have sprung unexpectedly out of investi- 
gations which might seem to the ignorant mere busy 
trifling, and which even those better able to judge could 
only regard with the intellectual interest whicli pure 
theoretical inquiry excites. 

Of all our members the eye has always been held the 
choicest gift of Nature the most marvellous product of 
her plastic force. Poets and orators have celebrated its 
praises; philosophers have extolled it as a crowning- 
instance of perfection in an organism ; and opticians have 
tried to imitate it as an unsurpassed model. And indeed 
the most enthusiastic admiration of this wonderful organ 
is only natural, when we consider what functions it per- 
forms ; when we dwell on its penetrating power, on the 
swiftness of succession of its brilliant pictures, and on 
the riches which it spreads before our sense. It is by 
the eye alone that we know the countless shining worlds 
that fill immeasurable space, the distant landscapes of 
our own earth, with all the varieties of sunlight that 
reveal them, the wealth of form and colour among 
flowers, the strong and happy life that moves in animals. 
Next to the loss of life itself that of eyesight is the 

But even more important, than the delight in beauty 
and admiration of majesty in the creation which we owe 
to the eye, is the security and exactness with which we 
can judge by sight of the position, distance, and size of 
the objects which surround us. For this knowledge is 
the necessary foundation for all our actions, from thread- 
ing a needle through a tangled skein of silk to leaping 
from cliff to cliff when life itself depends on the right 


measurement of the distance. In fact, the success of 
the movements and actions dependent on the accuracy 
of the pictures that the eye gives us forms a con- 
tinual test and con6rmation of that accuracy. If sight 
were to deceive us as to the position and distance of 
external objects, we should at once become aware of the 
delusion on attempting to grasp or to approach them. 
This daily verification .by our other senses of the im- 
pressions we receive by sight produces so firm a conviction 
of its absolute and complete truth that the exceptions 
taken by philosophy or physiology, however well grounded 
they may seem, have no power to shake it. 

No wonder then that, according to a wide-spread con- 
viction, the eye is looked on as an optical instrument 
so perfect that none formed by human hands can ever 
be compared with it, and that its exact and complicated 
construction should be regarded as the full explanation 
of the accuracy and variety of its functions. 

Actual examination of the performances of the eye as 
an optical instrument carried on chiefly during the last 
ten years has brought about a remarkable change in these 
views, just as in so many other cases the test of facts 
has disabused our minds of similar fancies. But as again 
in similar cases reasonable admiration rather increases 
than diminishes when really important functions are 
more clearly understood and their object better esti- 
mated, so it may well be with our more exact knowledge 
of the eye. For the great performances of this little 
organ can never be denied ; and while we might con- 
sider ourselves compelled to withdraw our admiration 
from one point of view, we must again experience it 
from another. 

Regarded as an optical instrument, the eye is a camera 
obscura. This apparatus is well known in the form used 
by photographers (Fig. 27). A box constructed of twc 



parts, of which one slides in the other, and blackened, 
has in front a combination of lenses fixed in the tube 
hi on the inside, which refract the incident rays of light, 
and unite them at the back of the instrument into an 
optical image of the objects which lie in front of the 
camera. When the photographer first arranges his instru- 
ment, he receives the image upon a plate of ground glass, 
g. It is there seen as a small and elaborate picture in 
its natural colours, more clear and beautiful than the 
most skilful painter could imitate, though indeed it is 
upside down. The next step is to substitute for this 

FIG. 27. 

glass a prepared plate upon which the light exerts a per- 
manent chemical effect, stronger on the more brightly 
illuminated parts, weaker on those which are darker. 
These chemical changes having once taken place are per- 
manent : by their means the image is fixed upon the plate. 
The natural camera obscura of the eye (seen in a 
diagrammatic section in Fig. 28) has its blackened 
chamber globular instead of cubical, and made not of 
wood, but of a thick, strong, white substance known as the 
sclerotic coat. It is this which is partly seen between 


the eyelids as 'the white of the eye.' This globular 
chamber is lined with a delicate coat of winding blood- 
vessels covered inside by black pigment. But the apple 
of the eye is not empty like the camera : it is filled with 
a transparent jelly as clear as water. The lens of the 
camera obscura is represented, first, by a convex trans- 
parent window like a pane of horn (the cornea), which 
is fixed in front of the sclerotic like a watch glass in front. 


of its metal case. This union and its own firm texture 
make its position and its curvature constant. But the 
glass lenses of the photographer are not fixed ; they are 
moveable by means of a sliding tube which can be ad- 
justed by a screw (Fig. 27, r\so as to bring the objects 
in front of the camera into focus. The nearer they are, 
the farther the lens is pushed forward ; the farther off, 
the more it is screwed in. The eye has the same task 
of bringing at one time near, at another distant, objects to 
a focus at the back of its dark chamber. So that some 


power of adjustment or 'accommodation' is necessary. 
This is accomplished by the movements of the crystalline 
lens (Fig. 28, L), which is placed a short distance behind 
the cornea. It is covered by a curtain of varying colour, 
the iris (J), which is perforated in the centre by a round 
hole, the pupil, the edges of which are in contact with the 
front of the lens. Through this opening we see through 
the transparent and, of course, invisible lens the black 
chamber within. The crystalline lens is circular, bi- 
convex, and elastic. It is attached at its edge to the 
inside of the eye by means of a circular band of folded 
membrane which surrounds it like a plaited ruff, and 
is called the ciliary body or Zonule of Zinn (Fig, 
28, * *). The tension of this ring (and so of the lens 
itself) is regulated by a series of muscular fibres known 
as the ciliary muscle (Cc). When this muscle con- 
tracts, the tension of the lens is diminished, and its sur- 
faces but chiefly the front one become by its physical 
property of elasticity more convex than when the eye 
is at rest ; its refractive power is thus increased, and the 
images of near objects are brought to a focus on the back 
of the dark chamber of the eye. 

Accordingly the healthy eye when at rest sees distant 
objects distinctly : by the contraction of the ciliary 
muscle it is 'accommodated' for those which are near. 
The mechanism by which this is accomplished, as above 
shortly explained, was one of the greatest riddles of the 
physiology of the eye since the time of Kepler ; and the 
knowledge of its mode of action is of the greatest prac- 
tical importance from the frequency of defects in the 
power of accommodation. No problem in optics has 
given rise to so many contradictory theories as this. The 
key to its solution was found when the French surgeon 
Sanson first observed very faint reflexions of light through 
the pupil from the two surfaces of the crystalline lens. 


and thus acquired the character of an unusually careful 
observer. For this phenomenon was anything but ob- 
vious ; it can only be seen by strong side illumination, 
in darkness otherwise complete, only when the observer 
takes a certain position, and then all he sees is a faint 
misty reflexion. But this faint reflexion was destined 
to become a shining light in a dark corner of science. It 
was in fact the first appearance observed in the living 
eye which came directly from the lens. Sanson imme- 
diately applied his discovery to ascertain whether the 
lens was in its place in cases of impaired vision. Max 
Langenbeck made the next step by observing that the 
reflexions from the lens alter during accommodation. 
These alterations were employed by Cramer of Utrecht, 
and also independently by the present writer, to arrive 
at an exact knowledge of all the changes which the lens 
undergoes during the process of accommodation. I suc- 
ceeded in applying to the inoveable eye in a modified 
form the principle of the heliometer, an instrument by 
which astronomers are able so accurately to measure small 
distances between stars in spite of their constant apparent 
motion in the heavens, that they can thus sound the 
depths of the region of the fixed stars. An instrument con- 
structed for the purpose, the ophthalmometer, enables 
us to measure in the living eye the curvature of the 
cornea, and of the two surfaces of the lens, the distance 
of these from each other, &c., with greater precision 
than could before be done even after death. By this 
means we can ascertain the entire range of the changes 
of the optical apparatus of the eye so far as it affects 

The physiological problem was therefore solved. Ocu- 
lists, and especially Donders, next investigated the indi- 
vidual defects of accommodation which give rise to the 
conditions known as long sight and short sight. It was 


necessary to devise trustworthy methods in order to 
ascertain the precise limits of the power of accommoda- 
tion even with inexperienced and uninstructed patients. 
It became apparent that very different conditions had 
been confounded as short sight and long sight, and this 
confusion had made the choice of suitable glasses un- 
certain. It was also discovered that some of the most 
obstinate and obscure affections of the sight, formerly 
reputed to be ' nervous,' simply depended on certain 
defects of accommodation, and could be readily removed 
by using suitable glasses. Moreover Bonders 1 proved 
that the same defects of accommodation are the most 
frequent cause of squinting, and Yon Graefe 2 had already 
shown that neglected and progressive shortsightedness 
tends to produce the most dangerous expansion and 
deformity of the back of the globe of the eye. 

Thus connections were discovered, where least expected, 
between' the optical discovery and important diseases, 
and the result was no less beneficial to the patient than 
interesting to the physiologist. 

We must now speak of the curtain which receives the 
optical image when brought to a focus in the eye. This 
is the retina, a thin membranous expansion of the optic 
nerve which forms the innermost of the coats of the eye. 
The optic nerve (Fig. 2, 0) is a cylindrical cord which 
contains a multitude of minute fibres protected by a 
strong tendinous sheath. The nerve enters the apple of 
the eye from behind, rather to the inner (nasal) side of 
the middle of its posterior hemisphere. Its fibres then 
spread out in all directions ov,er the front of the retina. 
They end by becoming connected, first, with ganglion cells 
and nuclei, like those found in the brain ; and, secondly, 

1 Professor of Physiology in the University of Utrecht. 

2 This great ophthalmic surgeon died in Berlin at the early age of forty-two 


with structures not elsewhere found, called rods and cones. 
The rods are slender cylinders ; the cones, or bulbs, some- 
what thicker, flask- shaped structures. All are ranged 
perpendicular to the surface of the retina, closely packed 
together, so as to form a regular mosaic layer behind it. 
Each rod is connected with one of the minutest nerve 
fibres, each cone with one somewhat thicker. This layer 
of rods and bulbs (also known as membrana Jacobi) has 
been proved by direct experiments to be the really sensi- 
tive layer of the retina, the structure in which alone 
the action of light is capable of producing a nervous 

There is in the retina a remarkable spot which is placed 
near its centre, a little to the outer (temporal) side, and 
which from its colour is called the yellow spot. The 
retina is here somewhat thickened, but in the middle of 
the yellow spot is found a depression, the fovea centralis, 
where the retina is reduced to those elements alone which 
are absolutely necessary for exact vision. Fig. 29, from 
Henle, shows a thin transverse section of this central de- 
pression made on a retina which had been hardened in 
alcohol. Lh (Lamina hyalina, membrana limitans) is 
an elastic membrane which divides the retina from the 
vitreous. The bulbs (seen at b) are here smaller than 
elsewhere, measuring only the 400th part of a millimeter 
in diameter, and form a close and regular mosaic. The 
other, more or less opaque, elements of the retina are 
seen to be wanting, except the corpuscles (^-), which 
belong to the cones. At / are seen the fibres which unite 
these with the rest of the retina. This consists of a layer 
3f fibres of the optic nerve (ri) in front, and two layers of 
nerve cells (gli and gle), known as the internal and exter- 
nal ganglion layers, with a stratum of fine granules (gri) 
between them. All these parts of the retina are absent 
at the bottom of the fovea centralis, and their gradual 



thinning away at its borders is seen in the diagram. Nor 
do the blood vessels of the retina enter the fovea, but end 
in a circle of delicate capillaries around it. 

This fovea, or pit of the retina, is of great importance 
for vision, since it is the spot where the most exact dis- 


crimination of distances is made. The cones are here 
packed most closely together, and receive light which has 
not been impeded by other semi-transparent parts of the 
retina. We may assume that a single nervous fibril runs 
from each of these cones through the trunk of the optic 
nerve to the brain, without touching its neighbours, and 
there produces its special impression, so that the excita- 
tion of each individual cone will produce a distinct and 
separate effect upon the sense. 

The production of optical images in a camera obscura 
depends on the well-known fact that the rays of light 
which come off from an illuminated object are so broken or 
refracted in passing through the lenses of the instrument, 
that they follow new directions which bring them all to a 
single point, the/ocus, at the back of the camera. A com- 
mon burning glass has the same property ; if we allow the 
rays of the sun to pass through it, and hold a sheet of white 
paper at the proper distance behind it, we may notice two 
effects. In the first place (and this is often disregarded) 
the burning lens, although made of transparent glass, 
throws a shadow like any opaque body ; and next we see 
in the middle of this shadow a spot of dazzling brilliance, 
the image of the sun. The rays which, if the lens had 
not been there, would have illuminated the whole space 
occupied by the shadow, are concentrated by the refracting 
power of the burning glass upon the bright spot in the 
middle, and so both light and heat are more intense there 
than where the unrefracted solar rays fall. If, instead of 
the disc of the sun, we choose a star -or any other point as 
the source of light, its light will be united into a point at 
the focus of the lens, and the image of the star will appear 
as such upon the white paper. If there is another fixed 
star near the one first chosen, its light will be collected at 
a second illuminated point on the paper ; and if the star 


happen to send out red rays, its image on the paper will 
also appear red. The same will be true of any number 
of neighbouring stars, the image of each corresponding 
to it in brilliance, colour, and relative position. And if, 
instead of a multitude of separate luminous points, we 
have a continuous series of them in a bright line or sur- 
face, a similar line or surface will be produced upon the 
paper. But here also, if the piece of paper be put to the 
proper distance, all the light that proceeds from any one 
point will be brought to a focus at a point which corre- 
sponds to it in strength and colour of illumination, and 
(as a corollary) no point of the paper receives light from 
more than a single point of the object. 

If now we replace our sheet of white paper by a pre- 
pared photographic plate, each point of its surface will be 
altered by the light which is concentrated on it. This 
light is all derived from the corresponding point in the 
object, and answers to it in intensity. Hence the changes 
which take place on the plate will correspond in amount 
to the chemical intensity of the rays which fall upon it. 

This is exactly what takes place in the eye. Instead 
of the burning glass we have the cornea and crystalline 
lens ; and instead of the piece of paper, the retina. Accord- 
ingly, if an optically accurate image is thrown upon the 
retina, each of its cones will be reached by exactly so 
much light as proceeds from the corresponding point in 
the field of vision ; and also the nerve fibre which arises 
from each cone will be excited only by the light proceeding 
from the corresponding point in the field, while other 
nerve fibres will be excited by the light proceeding from 
other points of the field. Fig. 30 illustrates this effect. 
The rays which come from the point A in the object of 
vision are so broken that they all unite at a on the retina, 
while those from B unite at b. Thus it results that the 
light of each separate bright point of the field of vision 


excites a separate impression ; that the difference of the 
several points of the field of vision in degree of brightness 
can be appreciated by the sense ; and lastly, that separate 
impressions may each arrive separately at the seat of 


If now we compare the eye with other optical instru- 
ments, we observe the advantage it has over them in its 
very large field of vision. This for each eye separately is 
160 (nearly two right angles) laterally, and 120 verti- 
cally, and for both together somewhat more than two 
right angles from right to left. The field of view of in- 

Fio. 30. 

struments made by art is usually very small, and becomes 
smaller with the increased size of the image. 

But we must also admit, that we are accustomed to 
expect in these instruments complete precision of the 
image in its entire extent, while it is only necessary for 
the image on the retina to be exact over a very small 
surface, namely, that of the yellow spot. The diameter 
of the central pit corresponds in the field of vision to an 
angular magnitude which can be covered by the nail of 
one's forefinger when the hand is stretched out as far as 
possible. In this small part of the field our power of 
vision is so accurate that it can distinguish the distance 
between two points, of only one minute angular magni- 
tude, i.e. a distance equal to the sixtieth part of the 
diameter of the finger-nail. This distance corresponds to 


the width of one of the cones of the retina. All the other 
parts of the retinal image are seen imperfectly, and the 
more so the nearer to the limit of the retina they fall. 
So that the image which we receive by the eye is like a 
picture, minutely and elaborately finished in the centre, 
but only roughly sketched in at the borders. But although 
at each instant we only see a very small part of the field 
of vision accurately, we see this in combination with 
what surrounds it, and enough of this outer and larger 
part of the field, to notice any striking object, and parti- 
cularly any change that takes place in it. All of this is 
unattainable in a telescope. 

But if the objects are too small, we cannot discern 
them at all with the greater part of the retina. 

When, lost in boundless blue on high, 
The lark pours forth his thrilling song, 1 

the ' ethereal minstrel ' is lost until we can bring her 
image to a focus upon the central pit of our retina. 
Then only are we able to see her. 

To look at anything means to place the eye in such a po- 
sition that the image of the object falls on the small region 
of perfectly clear vision. This we may call direct vision, 
applying the term indirect to that exercised with the 
lateral parts of the retina indeed with all except the 
yellow spot. 

The defects which result from the inexactness of vision 
and the smaller number of cones in the greater part of 
the retina are compensated by the rapidity with which we 
can turn the eye to one point after another of the field 
of vision, and it is this rapidity of movement which 

1 The lines in the well-known passage of Faust: 

"Wenn iiber uns im blauen Raum verloren 
Ihr schmetternd Lied die Lerche singt. 


really constitutes the chief advantage of the eye over 
other optical instruments. 

Indeed the peculiar way in which we are accustomed 
to give our attention to external objects, by turning it 
only to one thing at a time, and as soon as this has been 
taken in hastening to another, enables the sense of vision 
to accomplish as much as is necessary ; and so we have 
practically the same advantage as if we enjoyed an accu- 
rate view of the whole field of vision at once. It is not in 
fact until we begin to examine our sensations closely that 
we become aware of the imperfections of indirect vision. 
Whatever we want to see we look at, and see it accurately ; 
what we do not look at, we do not as a rule care for at 
the moment, and so do not notice how imperfectly we 
see it. 

Indeed, it is only after long practice that we are 
able to turn our attention to an object in the field of 
indirect vision (as is necessary for some physiological 
observations) without looking at it, and so bringing it 
into direct view. And it is just as difficult to fix the 
eye on an object for the number of seconds required to 
produce the phenomenon of an after-image. 1 To get 
this well defined requires a good deal of practice. 

A great part of the importance of the eye as an organ 
of expression depends on the same fact ; for the move- 
ments of the eyeball its glances are among the most 
direct signs of the movement of the attention, of the 
movements of the mind, of the person who is looking 
at us. 

Just as quickly as the eye turns upwards, downwards, 
and from side to side, does the accommodation change, 
so as to bring the object to which our attention is at 
the moment directed into focus ; and thus near and dis- 
tant objects pass in rapid succession into accurate view. 

1 Vide infra, p. 254. 


All these changes of direction and of accommodation 
take place far more slowly in artificial instruments. A 
photographic camera can never show near and distant 
objects clearly at once, nor can the eye; but the eye 
shows them so rapidly one after another that most people, 
who have not thought how they see, do not know that 
there is any change at all. 

Let us now examine the optical properties of the eye 
further. We will pass over the individual defects of 
accommodation which have been already mentioned as 
the cause of short and long sight. These defects appear 
to be partly the result of our artificial way of life, partly 
of the changes of old age. Elderly persons lose their 
power of accommodation, and their range of clear vision 
becomes confined within more or less narrow limits. To 
exceed these they must resort to the aid of glasses. 

But there is another quality which we expect of optical 
instruments, namely, that they shall be free from disper- 
sion that they be achromatic. Dispersion of light de- 
pends on the fact that the coloured rays which united 
make up the white light of the sun are not refracted in 
exactly the same degree by any transparent substance 
known. Hence the size and position of the optical 
images thrown by these differently coloured rays are not 
quite the same ; they do not perfectly overlap each other 
in the field of vision, and thus the white surface of the 
image appears fringedwith a violet or orange, according 
as the red or blue rays are broader. This of course takes 
off so far from the sharpness of the outline. 

Many of my readers know what a curious part the 
inquiry into the chromatic dispersion of the eye has 
played in the invention of achromatic telescopes. It is 
a celebrated instance of how a right conclusion may 
sometimes be. drawn from two false premisses. Newton 


thought he had discovered a relation between the re- 
fractive and dispersive powers of various transparent 
materials, from which it followed that no achromatic 
refraction was possible. Euler, 1 on the other hand, con- 
cluded that, since the eye is achromatic, the relation 
discovered by Newton could not be correct. Reasoning 
from this assumption, he constructed theoretical rules 
for making achromatic instruments, and Dolland 2 carried 
them out. But Dolland himself observed that the eye 
could not be achromatic, because its construction did not 
answer to Euler's rules ; and at last Fraunhofer 3 actually 
measured the degree of chromatic aberration of the eye. 
An eye constructed to bring red light from infinite dis- 
tance to a focus on the retina can only do the same with 
violet rays from a distance of two feet. With ordinary 
light this is not noticed because these extreme colours are 
the least luminous of all, and so the images they produce 
are scarcely observed beside the more intense images of 
the intermediate yellow, green, and blue rays. But the 
effect is very striking when we isolate the extreme rays 
of the spectrum by means of violet glass. Glasses 
coloured with cobalt oxide allow the red and blue rays 
to pass, but stop the green and yellow ones, that is, the 
brightest rays of the spectrum. If those of my readers 
who have eyes of ordinary focal distance will look at 
lighted street lamps from a distance with this violet 
glass, they will see a red flame surrounded by a broad 
bluish violet halo. This is the dispersive image of the 
flame thrown by its blue and violet light. The phe- 
nomenon is a simple and complete proof of the fact of 
chromatic aberration in the eye. 

Now the reason why this defect is so little noticed 

1 Leonard Euler born at Basel, 1707 ; died at St. Petersburgh, 1783. 

2 John Dolland, F.R.S. born 1706 ; died in London, 1761. 

3 Joseph Fraunhofer born in .Bavaria, 1787 ; died at Munich, 1826. 


under ordinary circumstances, and why it is in fact 
somewhat less than a glass instrument of the same 
construction would have, is that the chief refractive 
medium of the eye is water, which possesses a less dis- 
persive power than glass. 1 Hence it is that the chro- 
matic aberration of the eye, though present, does not 
materially affect vision with ordinary white illumination. 

A second defect which is of great importance in optical 
instruments of high magnifying power is what is known 
as spherical aberration. Spherical refracting surfaces 
approximately unite the rays which proceed from a lumin- 
ous point into a single focus, only when each ray falls 
nearly perpendicularly upon the corresponding part of 
the refracting surface. If all those rays which form the 
centre of the image are to be exactly united, a lens with 
other than spherical surfaces must be used, and this 
cannot be made with sufficient mechanical perfection. 
Now the eye has its refracting surfaces partly elliptical ; 
and so here again the natural prejudice in its favour led 
to the erroneous belief that spherical aberration was thus 
prevented. But this was a still greater blunder. More 
accurate investigation showed that much greater defects 
than that of spherical aberration are present in the eye, 
defects which are easily avoided with a little care in 
making optical instruments, and compared with which 
the amount of spherical aberration becomes very unim- 
portant. The careful measurements of the curvature of the 
cornea, first made by Senff of Dorpat, next, with a better 
adapted instrument, the writer's ophthalmometer already 
referred to, and afterwards carried out in numerous 
cases by Bonders, Knapp, and others, have proved that 
the cornea of most human eyes is not a perfectly sym- 

1 But still the diffraction in the eye is rather greater than an instrument 
made with water would produce under the same conditions. 


metrical curve, but is variously bent in different direc- 
tions. I have also devised a method of testing the 
4 centering ' of an eye during life, i.e. ascertaining whether 
the cornea and the crystalline lens are symmetrically 
placed with regard to their common axis. By this means 
I discovered in the eyes I examined slight but distinct 
deviations from accurate centering. ^ The result of these 
two defects of construction is the condition called astig- 
matism, which is found more or less in most human eyes, 
and prevents our seeing vertical and horizontal lines at 
the same distance perfectly clearly at once. If the degree 
of astigmatism is excessive, it can be obviated by the use 
of glasses with cylindrical surfaces, a circumstance which 
has lately much attracted the attention of oculists. 

Nor is this all. A refracting surface which is im- 
perfectly elliptical, an ill-centered telescope, does not 
give a single illuminated point as the image of a star, 

FIG. 31. 

but, according to the surface and arrangement of the 
refracting media, elliptic, circular, or linear images. Now 
the images of an illuminated point, as the human eye 
brings them to focus, are even more inaccurate : they are 
irregularly radiated. The reason of this lies in the con- 


stniction of the crystalline lens, the fibres of which are 
arranged around six diverging axes (shown in Fig. 31). So 
that the rays which we see around stars and other distant 
lights are images of the radiated structure of our lens ; 
and the universality of this optical defect is proved by any 
figure with diverging rays being called ' star-shaped.' It 
is from the same cause that the moon, while her crescent 
is still narrow, appears to many persons double or three- 

Now it is not too much to say that if an optician 
wanted to sell me an instrument which had all these 
defects, I should think myself quite justified in blaming 
his carelessness in the strongest terms, and giving him 
back his instrument. Of course, I shall not do this with 
my eyes, and shall be only too glad to keep them as long 
as I can defects and all. Still, the fact that, however 
bad they may be, I can get no others, does not at all 
diminish their defects, so long as I maintain the narrow 
but indisputable position of a critic on purely optical 

We have, however, not yet done with the list of the 
defects of the eye. 

We expect that the optician will use good, clear, per- 
fectly transparent glass for his lenses. If it is not so, 
a bright halo will appear around each illuminated surface 
in the image : what should be black looks grey, what 
should be white is dull. But this is just what occurs 
in the image our eyes give us of the outer world. The 
obscurity of dark objects when seen near very bright ones 
depends essentially on this defect; and if we throw a 
strong light l through the cornea and crystalline lens, 
they appear of a dingy white, less transparent than the 
' aqueous humour ' which lies between them. This defect 

1 Eg. from a lamp, concentrated by a bull's-eye condenser. 


is most apparent in the blue and violet rays of the solar 
spectrum ; for there comes in the phenomenon of fluo- 
rescence 1 to increase it. 

In fact, although the crystalline lens looks so beauti- 
fully clear when taken out of the eye of an animal just 
killed, it is far from optically uniform in structure. It 
is possible to see the shadows and dark spots within the 
eye (the so-called ' entoptic objects ') by looking at an 
extensive bright surface the clear sky, for instance 
through a very narrow opening. And these shadows are 
chiefly due to the fibres and spots in the lens. 

There are also a number of minute fibres, corpuscles 
and folds of membrane, which float in the vitreous 
humour, and are seen when they come close in front 
of the retina, even under the ordinary conditions of 
vision. They are then called muscce volitantes, because 
when the observer tries to look 2 at them, they naturally move 
with the movement of the eye. They seem continually 
to flit away from the point of vision, and thus look like 
flying insects. These objects are present in everyone's 
eyes, and usually float in the highest part of the globe of 
the eye, out of the field of vision, whence on any sudden 
movement of the eye they are dislodged and swim freely 
in the vitreous humour. They may occasionally pass in 
front of the central pit, and so impair sight. It is a 

1 This term is given to the property which certain substances possess of 
becoming for a time faintly luminous as long as they receive violet and 
blue light. The bluish tint of a solution of quinine, and the green colour 
of uranium glass, depend on this property. The fluorescence of the cornea 
and crystalline lens appears to depend upon the presence in their tissue of 
a very small quantity of a substance like quinine. For the physiologist 
this property is most valuable, for by its aid he can see the lens in a living 
eye by throwing on it a concentrated beam of blue light, and thus ascertain 
that it is placed close behind the iris, not separated by a large ' posterior 
chamber,' as was long supposed. But for seeing, the fluorescence of the 
cornea and lens is simply disadvantageous. 

8 Vide supra, p. 213. 


remarkable proof of the way in which we observe, or fail 
to observe, the impressions made on our senses, that these 
muscce volitantes often appear some-thing quite new and 
disquieting to persons whose sight is beginning to suffer 
from any cause ; although, of course, there must have been 
the same conditions long before. 

A knowledge of the way in which the eye is developed 
in man and other vertebrates explains these irregularities 
in the structure of the lens and the vitreous body. Both 
are produced by an invagination of the integument of the 
embryo. A dimple is first formed, this deepens to a round 
pit, and then expands until its orifice becomes relatively 
minute, when it is finally closed and the pit becomes 
completely shut oft*. The cells of the scarf-skin which 
line this hollow form the crystalline lens, the true skin 
beneath them becomes its capsule, and the loose tissue 
which underlies the skin is developed into the vitreous 
humour. The mark where the neck of the fossa was sealed 
is still to be recognised as one of the ' entoptic images ' of 
many adult eyes. 

The last defect of the human eye which must be noticed 
is the existence of certain inequalities of the surface which 
receives the optical image. Not far from the centre of 
the field of vision there is a break in the retina, where 
the optic nerve enters. Here there is nothing but nerve 
fibres and blood-vessels ; and, as the cones are absent, any 
rays of light which fall on the optic nerve itself are un- 
perceived. This 'blind spot' will therefore produce a corre- 
sponding gap in the field of vision where nothing will be 
visible. Fig. 32 shows the posterior half of the globe of a 
right eye which has been cut across. E is the retina with 
its branching blood-vessels. The point from which these 
diverge is that at which the optic nerve enters. To the 
reader's left is seen the ' yellow spot.' 


Now the gap caused by the presence of the optic nerve 
is no slight one. It is about 6 in .horizontal and 8 in 
vertical dimension. Its inner border is about 12 hori- 
zontally distant from the temporal ' or external side of 
the centre of distinct vision. The way to recognise 
this blind spot most readily is doubtless known to many 
of my readers. Take a sheet of white paper and mark on 
it a little cross ; then to the right of this, on the same 
level, and about three inches off, draw a round black spot 

S Ch 

FIG. 32. 

half an inch in diameter. Now, holding the paper at 
arm's length, shut the left eye, fix the right upon the 
cross, and bring the paper gradually 1 nearer. When it is 
about eleven inches from the eye, the black spot will 
suddenly disappear, and will again come into sight as the 
paper is moved nearer. 

This blind spot is so large that it might prevent our 
seeing eleven full moons if placed side by side, or a man's 
face at a distance of only six or seven feet. Mariotte, 1 who 
liscovered the phenomenon, amused Charles II. and his 

1 Edme. Mariotte Lorn in Burgundy, died at Paris, 1684. 


courtiers by showing them how they might see each other 
with their heads cut off. 

There are, in addition, a number of smaller gaps in the 
field of vision, in which a small bright point, a fixed star 
for example, may be lost. These are caused by the blood- 
vessels of the retina. The vessels run in the front layers, 
and so cast their shadow on the part of the sensative 
mosaic which lies behind them. The larger ones shut off 
the light from reaching the rods and cones altogether, the 
more slender at least limit its amount. 

These splits in the picture presented by the eye may be 
recognised by making a hole in a card with a fine needle, 
and looking through it at the sky, moving the card a little 
from side to side all the time. A still better experiment 
is to throw sunlight through a small lens upon the white 
of the eye at the outer angle (temporal canthus), while 
the globe is turned as much as possible inwards. The 
shadow of the blood-vessels is then thrown across on to 
the inner wall of the retina, and we see them as gigantic 
branching lines, like fig. 32 magnified. These vessels lie 
in the front layer of the retina itself, and, of course, their 
shadow can only be seen when it falls on the proper sensi- 
tive layer. So that this phenomenon furnishes a proof 
that the hindmost layer is that which is sensitive to light. 
And by its help it has become possible actually to measure 
the distance between the sensitive and the vascular layers 
of the retina. It is done as follows : 

If the focus of the light thrown on to the white of the eye 
(the sclerotic) is moved slightly backwards and forwards, 
the shadow of the blood-vessels and its image in the field 
of vision will, of course, move also. The extent of these 
movements can be easily measured, and from these data 
Heinrich Miiller, of Wiirzburg whose too early loss to 
science we still deplore determined the distance between 
the two foci, and found it exactly to equal the thickness 


which actually separates the layer of rods and cones from 
the vascular layer of the retina. 

The condition of the point of clearest vision (the yellow 
spot) is disadvantageous in another way. It is less sensi- 
tive to weak light than the other parts of the retina. It 
has been long known that many stars of inferior magni- 
tude for example, the Coma Berenice? and the Pleiades 
are seen more brightly if looked at somewhat obliquely 
than when their rays fall full upon the eye. This can be 
proved to depend partly on the yellow colour of the 
macula, which weakens blue more than other rays. It may 
also be partly the result of the absence of vessels at this 
yellow spot which has been noticed above, which interferes 
with its free communication with the life-giving blood. 

All these imperfections would be exceedingly trouble 
some in an artificial camera obscura and in the photographic 
picture it produced. But they are not so in the eye so 
little, indeed, that it was very difficult to discover some 
of them. The reason of their not interfering with our 
perception of external objects is not simply that we have 
two eyes, and so one makes up for the defects of the other. 
For even when we do not use both, and in the case of 
persons blind of one eye, the impression we receive from 
the field of vision is free from the defects which the 
irregularity of the retina would otherwise occasion. The 
chief reason is that we are continually moving the eye, 
and also that the imperfections almost always affect those 
parts of the field to which we are not at the moment 
directing our attention. 

But, after all it remains a wonderful paradox, that 
we are so slow to observe these and other peculiarities 
of vision (such as the after-images of bright objects), so 
long as they are not strong enough to prevent our seeing 


external objects. It is a fact which we constantly meet, 
not only in optics, but in studying the perceptions pro- 
duced by other senses on the consciousness. The diffi- 
culty with which we perceive the defect of the blind 
spot is well shown by the history of its discovery. Its 
existence was first demonstrated by theoretical arguments. 
While the long controversy whether the perception of 
light resided in the retina or the choroid was still unde- 
cided, Mariotte asked himself what perception there was 
where the choroid is deficient. He made experiments to 
ascertain this point, and in the course of them discovered 
the blind spot. Millions of men had used their eyes for 
ages, thousands had thought over the nature and cause 
of their functions, and, after all, it was only by a remark- 
able combination of circumstances that a simple pheno- 
menon was noticed which would apparently have revealed 
itself to the slightest observation. Even now, anyone 
who tries for the first time to repeat the experiment which 
demonstrates the existence of the blind spot, finds it diffi- 
cult to divert his attention from the fixed point of clear 
vision, without losing sight of it in the attempt. Indeed, 
it is only by long practice in optical experiments that 
even an experienced observer is able, as soon as he shuts 
one eye, to recognise the blank space in the field of vision 
which corresponds to the blind spot. 

Other phenomena of this kind have only been discovered 
by accident, and usually by persons whose senses were 
peculiarly acute, and whose power of observation was 
unusually stimulated. Among these may be mentioned 
Goethe, Purkinje, 1 and Johannes Miiller. 2 When a sub- 

1 A distinguished embryologist, for many years professor at Breslau : 
he died at Prague, 1869, set. 82. 

2 A great biologist, in the full sense of the term. He was professor of 
physiology at Berlin, and died 1858, set. 57. His Manual of Physiology 
was translated into English by the late Dr. Baly. TB. 


sequent observer tries to repeat on his own eyes these 
experiments as he finds them described, it is of course 
easier for him than for the discoverer ; but even now there 
are many of the phenomena described by Purkinje which 
have never been seen by anyone else, although it cannot 
be certainly held that they depended on individual pecu- 
liarities of this acute observer's eyes. 

The phenomena of which we have spoken, and a number 
of others also, may be explained by the general rule that 
it is much easier to recognise any change in the condi- 
tion of a nerve than a constant and equable impression 
on it. In accordance with this rule, all peculiarities in 
the excitation of separate nerve fibres, which are equally 
present during the whole of life (such as the shadow of 
the blood-vessels of the eye, the yellow colour of the cen- 
tral pit of the retina, and most of the fixed entoptic 
images), are never noticed at all ; and if we want to 
observe them we must employ unusual modes of illumina- 
tion and, particularly, constant change of its direction. 

According to our present knowledge of the conditions 
of nervous excitation, it seems to me to be very unlikely 
that we have here to do with a simple property of sensa- 
tion ; it must, I think, be rather explained as a pheno- 
menon belonging to our power of attention, and I now 
only refer to the question in passing, since its full discus- 
sion will come afterwards in its proper connection. 

So much for the physical properties of the Eye. If I 
am asked why I have spent so much time in explaining 
its imperfection to my readers, I answer, as I said at first, 
that I have not done so in order to depreciate the perfor- 
mances of this wonderful organ or to diminish our admi- 
ration of its construction. It was my object to make the 
reader understand, at the first step of our inquiry, that it 


is not any mechanical perfection of the organs of our 
senses which secures for us such wonderfully true and exact 
impressions of the outer world. The next section of this 
inquiry will introduce much bolder and more para- 
doxical conclusions than any I have yet stated. We have 
now seen that the eye in itself is not by any means so 
complete an optical instrument as it first appears : its 
extraordinary value depends upon the way in which we 
use it : its perfection is practical, not absolute, consisting 
not in the avoidance of every error, but in the fact that 
all its defects do not prevent its rendering us the most 
important and varied services. 

From this point of view, the study of the eye gives us 
a deep insight into the true character of organic adapta- 
tion generally. And this consideration becomes still more 
interesting when brought into relation with the great and 
daring conceptions which Darwin has introduced into 
science, as to the means by which the progressive perfec- 
tion of the races of animals and plants has been carried 
on. Wherever we scrutinise the construction of physio- 
logical organs, we find the same character of practical 
adaptation to the wants of the organism ; although, per- 
haps, there is no instance which we can follow out so 
minutely as that of the eye. 

For the eye has every possible defect that can be found 
in an optical instrument, and even some which are peculiar 
to itself ; but they are all so counteracted, that the inexact- 
ness of the image which results from their presence very 
little exceeds, under ordinary conditions of illumination, 
fche limits which are set to the delicacy of sensation by 
the dimensions of the retinal cones. But as soon as we 
make our observations under somewhat changed condi- 
tions, we become aware of the chromatic aberration, the 
astigmatism, the blind spots, the venous shadows, the 


imperfect transparency of the media, and all the other 
defects of which I have spoken. 

The adaptation of the eye to its function is, therefore, 
most complete, and is seen in the very limits which 
are set to its defects. Here the result which may be 
reached by innumerable generations working under the 
Darwinian law of inheritance, coincides with what the 
wisest Wisdom may have devised beforehand. A sensible 
man will not cut firewood with a razor, and so we may 
assume that each step in the elaboration of the eye must 
have made the organ more vulnerable and more slow in 
its development. We must also bear in mind that soft, 
watery animal textures must always be unfavourable and 
difficult material for an instrument of the mind. 

One result of this mode of construction of the eye, of 
which we shall see the importance bye and bye, is that 
clear and complete apprehension of external objects by 
the sense of sight is only possible when we direct our 
attention to one part after another of the field of vision 
in the manner partly described above. Other conditions, 
which tend to produce the same limitation, will after- 
wards come under our notice. 

But, apparently, we are not yet come much nearer to un- 
derstanding sight. We have only made one step : we have 
learnt how the optical arrangement of the eye renders it 
possible to separate the rays of light which come in from 
all parts of the field of vision, and to bring together again 
all those that have proceeded from a single point, so 
that they may produce their effect upon a single fibre of 
the optic nerve. 

Let us see, therefore, how much we know of the sensa- 
tions of the eye, and how far this will bring us towards the 
solution of the problem. 


IN the first section of our subject we have followed the 
course of the rays of light as far as the retina, and seen 
what is the result produced by the peculiar arrangement 
of the optical apparatus. The light which is reflected 
from the separate illuminated points of external objects 
is again united in the sensitive terminal structures of 
separate nerve fibres, and thus throws them into action 
without affecting their neighbours. At this point the 
older physiologists thought they had solved the problem, 
so far as it appeared to them to be capable of solution. 
External light fell directly upon a sensitive nervous 
structure in the retina, and was, as it seemed, directly 
felt there. 

But during the last century, and still more during the 
first quarter of this, our knowledge of the processes which 
take place in the nervous system was so far developed, 
that Johannes Miiller, as early as the year 1826, 1 when 
writing that great work on the ' Comparative Physiology 
of Vision,' which marks an epoch in science, was able to 
lay down the most important principles of the theory of 
the impressions derived from the senses. These prin- 
ciples have not only been confirmed in all important 
points by subsequent investigation, but have proved of 
even more extensive application than this eminent physio- 
logist could have suspected. 

The conclusions which he arrived at are generally com- 
prehended under the name of the theory of the Specific 

1 The year in which he was appointed Extraordinary Professor of Phy- 
siology in the University of Bonn. 


Action of the Senses. They are no longer so novel that 
they can be reckoned among the latest advances of the 
theory of vision, which form the subject of the present 
essay. Moreover, they have been frequently expounded 
in a popular form by others as well as by myself. 1 But 
that part of the theory of 'vision with which we are now 
occupied is little more than a further development of the 
theory of the specific action of the senses. I must, there- 
fore, beg my reader to forgive me if, in order to give him 
a comprehensive view of the whole subject in its proper 
connection, I bring before him much which he already 
knows, while I also introduce the more recent additions 
to our knowledge in their appropriate places. 

All that we apprehend of the external world is brought 
to our consciousness by means of certain changes which 
are produced in our organs of sense by external impres- 
sions, and transmitted to the brain by the nerves. It is 
in the brain that these impressions first become conscious 
sensations, and are combined so as to produce our concep- 
tions of surrounding objects. If the nerves which convey 
these impressions to the brain are cut through, the sensa- 
tion, and the perception of the impression, immediately 
cease. In the case of the eye, the proof that visual per- 
ception is not produced directly in each retina, but only 
in the brain itself by means of the impressions transmitted 
to it from both eyes, lies in the fact (which I shall after- 
wards more fully explain) that the visual impression of 
any solid object of three dimensions is only produced by 
the combination of the impressions derived from both 

What, therefore, we directly apprehend is not the imme- 
diate action of the external exciting cause upon the ends 

1 ' On the Nature of Special Sensations in Man,' Kbnigsberger naturwis- 
senschaftliche Unterhaltungen, vol. iii. 1852. ' Human Vision,' a popular 
Scientific Lecture by H. Helmholtz, Leipzig, 1855. 


of our nerves, but only the changed condition of the 
nervous fibres which we call the state of excitation or 
functional activity. 

Now all the nerves of the body, so far as we at present 
know, have the same structure, and the change which we 
call excitation is in each of them a process of precisely 
the same kind, whatever be the function it subserves. For 
while the task of some nerves is that already mentioned, 
of carrying sensitive impressions from the external organs 
to the brain, others convey voluntary impulses in the 
opposite direction, from the brain to the muscles, caus- 
ing them to contract, and so moving the limbs. Other 
nerves, again, carry an impression from the brain to 
certain glands, and call forth their secretion, or to the 
heart and to the blood-vessels, and regulate the circula- 
tion. But the fibres of all these nerves are the same 
clear, cylindrical threads of microscopic minuteness, con- 
taining the same oily and albuminous material. It is 
true that there is a difference in the diameter of the 
fibres, but this, so far as we know, depends only upon 
minor causes, such as the necessity of a certain strength 
and of getting room for a certain number of independent 
conducting fibres. It appears to have no relation to their 
peculiarities of function. 

Moreover, all nerves have the same electro-motor 
actions, as the researches of Du Bois Reymond l prove. 
In all of them the condition of excitation is called forth 
by the same mechanical, electrical, chemical, or thermo- 
metric changes. It is propagated with the same rapidity, 
of about one hundred feet in the second, to each end of 
the fibres, and produces the same changes in their electro- 
motor properties. Lastly, all nerves die when sub- 
mitted to like conditions, and, with a slight apparent dif- 

1 Professor of Physiology in the University of Berlin. 


ference according to their thickness, undergo the same 
coagulation of their contents. In short, all that we can 
ascertain of nervous structure and function, apart from the 
action of the other organs with which they are united and 
in which during life we see the proofs of their activity, is 
precisely the same for all the different kinds of nerves. 
Very lately the French physiologists, Philippeau and 
Vulpian, after dividing the motor and sensitive nerves of 
the tongue, succeeded in getting the upper half of the 
sensitive nerve to unite with the lower half of the motor. 
After the wound had healed, they found that irritation of 
the upper half, which in normal conditions would have 
been felt as a sensation, now excited the motor branches 
below, and thus caused the muscles of the tongue to 
move. We conclude from these facts that all the differ- 
ence which is seen in the excitation of different nerves 
depends only upon the difference of the organs to which 
the nerve is united, and to which it transmits the state 
of excitation. 

The nerve-fibres have been often compared with tele- 
graphic wires traversing a country, and the comparison is 
well fitted to illustrate this striking and important pecu- 
liarity of their mode of action. In the net-work of tele- 
graphs we find everywhere the same copper or iron wires 
carrying the same kind of movement, a stream of elec- 
tricity, but producing the most different results in the 
various stations according to the auxiliary apparatus with 
which they are connected. At one station the effect is 
the ringing of a bell, at another a signal is moved, and at 
a third a recording instrument is set to work. Chemical 
decompositions may be produced which will serve to spell 
out the messages, and even the human arm may be moved 
by electricity so as to convey telegraphic signals. When 
the Atlantic cable was being laid, Sir William Thomson 
found that the slightest signals could be recognised by the 


sense of taste, if the wire was laid upon the tongue. Or, 
again, a strong electric current may be transmitted by 
telegraphic wires in order to ignite gunpowder for blasting 
rocks. In short, everyone of the hundred different actions 
which electricity is capable of producing may be called 
forth by a telegraphic wire laid to whatever spot we 
please, and it is always the same process in the wire itself 
which leads to these diverse consequences. Nerve-fibres 
and telegraphic wires are equally striking examples to 
illustrate the doctrine that the same causes may, under 
different conditions, produce different results. However 
commonplace this may now sound, mankind had to work 
long and hard before it was understood, and before this 
doctrine replaced the belief previously held in the constant 
and exact correspondence between cause and effect. And 
we can scarcely say that the truth is even yet universally 
recognised, since in our present subject its consequences 
have been till lately disputed. 

Therefore, as motor nerves, when irritated, produce 
movement, because they are connected with muscles, 
and glandular nerves secretion, because they lead to 
glands, so do sensitive nerves, when they are irritated, 
produce sensation, because they are connected with sensi- 
tive organs. But we have very different kinds of sensa- 
tion. In the first place, the impressions derived from 
external objects fall into five groups, entirely distinct 
from each other. These correspond to the five senses, and 
' their difference is so great that it is not possible to com- 
pare in quality a sensation of light with one of sound 
or of smell. We will name this difference, so much 
deeper than that between comparable qualities, a differ- 
ence of the mode, or kind, of sensation, and will describe 
the differences between impressions belonging to the same 
sense (for example, the difference between the various 
sensations of colour) as a difference of quality. 


Whether by the irritation of a nerve we produce a 
muscular movement, a secretion or a sensation depends 
upon whether we are handling a motor, a glandular, or a 
sensitive nerve, and not at all upon what means of irrita- 
tion we may use. It may be an electrical shock, or tearing 
the nerve, or cutting it through, or moistening it with a 
solution of salt, or touching it with a hot wire. In the 
same way (and this great step in advance was due to 
Johannes Miiller) the land of sensation which will ensue 
when we irritate a sensitive nerve, whether an impression 
of light, or of sound, or of feeling, or of smell, or of taste, 
will be produced, depends entirely upon which sense the 
excited nerve subserves, and not at all upon the method 
of excitation we adopt. 

Let us now apply this to the optic nerve, which is the 
object of our present enquiry. In the first place, we 
know that no kind of action upon any part of the body 
except the eye and the nerve which belongs to it, can 
ever produce the sensation of light. The stories of som- 
nambulists, which are the only arguments that can be 
adduced against this belief, we may be allowed to dis- 
believe. But, on the other hand, it is not light alone 
which can produce the sensation of light upon the eye, 
but also any other power which can excite the optic 
nerve. If the weakest electrical currents are passed 
through the eye they produce flashes of light. A blow, 
or even a slight pressure made upon the side of the eye- 
ball with the finger, makes an impression of light in the 
darkest room, and, under favourable circumstances, this 
may become intense. In these cases it is important to 
remember that there is no objective light produced in 
the retina, as some of the older physiologists assumed, 
for the sensation of light may be so strong that a se- 
cond observer could not fail to see through the pupil the 
illumination of the retina which would follow, if the 


sensation were really produced by an actual development 
of light within the eye. But nothing of the sort has 
ever been seen. Pressure or the electric current excites 
the optic nerve, and therefore, according to Miiller's 
law, a sensation of light results, but under these cir- 
cumstances, at least, there is not the smallest spark of 
actual light. 

In the same way, increased pressure of blood, its ab- 
normal constitution in fevers, or its contamination with 
intoxicating or narcotic drugs, can produce sensations of 
light to which no actual light corresponds. Even in 
cases in which an eye is entirely lost by accident or by 
an operation, the irritation of the stump of the optic 
nerve while it is healing is capable of producing similar 
subjective effects. It follows from these facts that the 
peculiarity in kind which distinguishes the sensation of 
light from all others does not depend upon any peculiar 
qualities of light itself. Every action which is capable 
of exciting the optic nerve is capable of producing the 
impression of light ; and the purely subjective sensation 
thus produced is so precisely similar to that caused by ex- 
ternal light, that persons unacquainted with these pheno- 
mena readily suppose that the rays they see are real ob- 
jective beams. 

Thus we see that external light produces no other 
effects in the optic nerve than other agents of an entirely 
different nature. In one respect only does light differ 
from the other causes which are capable of exciting this 
nerve : namely, that the retina, being placed at the back 
of the firm globe of the eye, and further protected by 
the bony orbit, is almost entirely withdrawn from other 
exciting agents, and is thus only exceptionally affected 
by them, while it is continually receiving the rays of 
light which stream in upon it through the transparent 
media of the eye. 


On the other hand, the optic nerve, by reason of the 
peculiar structures in connection with the ends of its 
fibres, the rods and cones of the retina, is incomparably 
more sensitive to rays of light than any other nervous 
apparatus of the body, since the rest can only be affected 
by rays which are concentrated enough to produce notice- 
able elevation of temperature. 

This explains why the sensations of the optic nerve are 
for us the ordinary sensible sign of the presence of light 
in the field of vision, and why we always connect the sen- 
sation of light with light itself, even where they are really 
unconnected. But we must never forget that a survey of 
all the facts in their natural connection puts it beyond 
doubt that external light is only one of the exciting 
causes capable of bringing the optic nerve into func- 
tional activity, and therefore that there is no exclusive 
relation between the sensation of light and light itself. 

Now that we have considered the action of excitants 
upon the optic nerve in general, we will proceed to the 
qualitative differences of the sensation of light, that is 
to say, to the various sensations of colour. We will try to 
ascertain how far these differences of sensation correspond 
to actual differences in external objects. 

Light is known in Physics as a movement which is 
propagated by successive waves in the elastic ether distri- 
buted through the universe, a movement of the same kind 
as the circles which spread upon the smooth surface of a 
pond when a stone falls on it, or the vibration which is 
transmitted through our atmosphere as sound. The chief 
difference is, that the rate with which light spreads, and 
the rapidity of movement of the minute particles which 
form the waves of ether, are both enormously greater than 
that of the waves of water or of air. The waves of light 
sent forth from the sun differ exceedingly in size, just as 


the little ripples whose summits are a few inches distant 
from each other differ from the waves of the ocean, be- 
tween whose foaming crests lie valleys of sixty or a hun- 
dred feet. But, just as high and low, short and long waves, 
on the surface of water, do not differ in kind, but only in 
size, so the various waves of light which stream from the 
sun differ in their height and length, but move all in the 
same manner, and show (with certain differences depend- 
ing upon the length of the waves) the same remark- 
able properties of reflection, refraction, interference, dif- 
fraction, and polarisation. Hence we conclude that the 
undulating movement of the ether is in all of them the 
same. We must particularly note that the phenomena 
of interference, under which light is now strengthened, 
and now obscured by light of the same kind, according 
to the distance it has traversed, prove that all the rays of 
light depend upon oscillations of waves ; and further, that 
the phenomena of polarisation, which differ according to 
different lateral directions of the rays, show that the par- 
ticles of ether vibrate at right angles to the direction in 
which the ray is propagated. 

All the different sorts of rays which I have mentioned 
produce one effect in common. They raise the tempera- 
ture of the objects on which they fall, and accordingly 
are all felt by our skin as rays of heat. 

On the other hand, the eye only perceives one part of 
these vibrations of ether as light. It is not at all cogni- 
sant of the waves of great length, which I have compared 
with those of the ocean ; these, therefore, are named the 
dark heat-rays. Such are those which proceed from a 
warm but not red-hot stove, and which we recognise as 
heat, but not as light. 

Again, the waves of shortest length, which correspond 
with the very smallest ripples produced by a gentle breeze, 
are so slightly appreciated by the eye, that such rays are 


also generally regarded as invisible, and are known as the 
dark chemical rays. 

Between the very long and the very short waves of 
ether there are waves of intermediate length, which 
strongly affect the eye, but do not essentially differ in 
any other physical property from the dark rays of heat 
and the dark chemical rays. The distinction between the 
visible and invisible rays depends only on the different 
length of their waves and the different physical relations 
which result therefrom. We call these middle rays Light, 
because they alone illuminate our eyes. 

When we consider the heating property of these rays 
we also call them luminous heat ; and because they pro- 
duce such a very different impression on our skin and on 
our eyes, heat was universally considered as an entirely 
different kind of radiation from light, until about thirty 
years ago. But both kinds of radiation are inseparable 
from one another in the illuminating rays of the sun ; 
indeed, the most careful recent investigations prove that 
they are precisely identical. To whatever optical pro- 
cesses they may be subjected, it is impossible to weaken 
their illuminating power without at the same time, and 
in the same degree, diminishing their heating and their 
chemical action. Whatever produces an undulatory move- 
ment of ether, of course produces thereby all the effects 
of the undulation, whether light, or heat, or fluorescence, 
or chemical change. 

Those undulations which strongly affect our eyes, and 

'which we call light, excite the impression of different 

colours, according to the length of the waves. The un- 

f dulations with the longest waves appear to us red ; and 

as the length of the waves gradually diminishes they 

seem to be golden-yellow, yellow, green, blue, violet, the 

last colour being that of the illuminating rays which 


Lave the smallest wave-length. This series of colours is 
universally known in the rainbow. We also see it if we 
look towards the light through a glass prism, and a dia- 
mond sparkles with hues which follow in the same order. 
In passing through transparent prisms, the primitive 
beam of white light, which consists of a multitude of 
rays of various colour and various wave-length, is de- 
composed by the different degree of refraction of its 
several parts, referred to in the last essay ; and thus 
each of its component hues appears separately. These 
colours of the several primary forms of light are best 
seen in the spectrum produced by a narrow streak of light 
passing through a glass prism : they are at once the fullest 
and the most brilliant which the external world can show. 
. When several of these colours are mixed together, they 
give the impression of a new colour, which generally 
seems more or less white. If they were all mingled in 
precisely the same proportions in which they are com- 
bined in the sun-light, they would give the impression of 
perfect white. According as the rays of greatest, middle, 
or least wave-length predominate in such a mixture, it 
appears as reddish-white, greenish-white, bluish-white, 
and so on. 

Everyone who has watched a painter at work knows 
that two colours mixed together give a new one. Now, 
although the results of the mixture of coloured light 
differ in many particulars from those of the mixture of 
pigments, yet on the whole the appearance to the eye is 
similar in both cases. If we allow two different coloured 
lights to fall at the same time upon a white screen, or 
upon the same part of our retina, we see only a single 
compound colour, more or less different from the two 
original ones. 

The most striking difference between the mixture of 
pigments and that of coloured light is, that while 


painters make green by mixing blue and yellow pig- 
ments, the union of blue and yellow rays of light pro- 
duces white. The simplest way of mixing coloured light 
is shown in Fig. 33. P is a small flat piece of glass ; b and 
g are two coloured wafers. The 
observer looks at b through the 
glass plate, while g is seen re- 
flected in the same ; and if g is 
put in a proper position, its image 

\x i exactly coincides with that of b. 

It then appears as if there was 
a single wafer at 6, with a colour 

produced by the mixture of the two real ones. In this 
experiment the light from 6, which traverses the glass 
pane, actually unites with that from #, which is reflected 
from it, and the two combined pass on to the retina at 
o. In general, then, light, which consists of undu- 
lations of different wave-lengths, produces different im- 
pressions upon our eye, namely, those of different colours. 
But the number of hues which we can recognise is 
much smaller than that of the various possible com- 
binations of rays with different wave-lengths which ex- 
ternal objects can convey to our eyes. The retina 
cannot distinguish between the white which is pro- 
duced by the union of scarlet and bluish-green light, 
and that which is composed of yellowish-green and 
violet, or of yellow and ultramarine blue, or of red, 
green, and violet, or of all the colours of the spectrum 
united. All these combinations appear identically as 
white ; and yet, from a physical point of view, they are 
very different. In fact, the only resemblance between 
the several combinations just mentioned is, that they are 
indistinguishable to the human eye. For instance, a sur- 
face illuminated with red and bluish-green light would 
come out black in a photograph ; while another lighted 


with yellowish green and violet would appear very bright, 
although both surfaces alike seem to the eye to be simply 
white. Again, if we successively illuminate coloured ob- 
jects with white beams of light of various composition, 
they will appear differently coloured. And whenever we 
decompose two such beams by a prism, or look at them 
through a coloured glass, the difference between them at 
once becomes evident. 

Other colours, also, especially when they are not 
strongly pronounced, may, like pure white light, be 
composed of very different mixtures, and yet appear in- 
distinguishable to the eye, while in every other property, 
physical or chemical, they are entirely distinct. 

Newton first showed how to represent the system of 
colours distinguishable to the eye in a simple diagram- 
matic form ; and by the same means it is comparatively 
easy to demonstrate the law of the combination of colours. 
The primary colours of the spectrum are arranged in a 
series around the circumference of a circle, beginning with 
red, and by imperceptible degrees passing through the 
various hues of the rainbow to violet. The red and violet 
are united by shades of purple, which on the one side pass 
off to the indigo and blue tints, and on the other through 
crimson and scarlet to orange. The middle of the circle 
is left white, and on lines which run from the centre to 
the circumference are represented the various tints which 
can be produced by diluting the full colours of the cir- 
cumference until they pass into white. A colour-disc of 
this kind shows all the varieties of hue which can be 
produced with the same amount of light. 

It will now be found possible so to arrange the places 
of the several colours in this diagram, and the quantity 
of light which each reflects, that when we have ascer- 
tained the resultants of two colours of different known 


strength of light (in the same way as we might determine 
the centre of gravity of two bodies of different known 
weights), we shall then find their combination-colour 
at the ' centre of gravity ' of the two amounts of light. 

FIG. 34. 



Pu rple 


That is to say, that in a properly constructed colour-disc, 
the combination-colour of any two colours will be found 
upon a straight line drawn from between them ; and com- 
pound colours which contain more of one than of the 
other component hue, will be found in that proportion 
nearer to the former, and further from the latter. 

We find, however, when we have drawn our diagram, 
that those colours of the spectrum which are most satu- 
rated in nature, and which must therefore be placed at 
the greatest distance from the central white, will not 
arrange themselves in the form of a circle. The circum- 
ference of the diagram presents three projections cor- 
responding to the red, the green, and the violet, so that 
the colour circle is more properly a triangle, with the 
corners rounded off, as seen in Fig. 34. The continuous 
line represents the curve of the colours of the spectrum, 
and the small circle in the middle the white. At the cor- 


ners are the three colours I have mentioned, 1 and the sides 
of the triangle show the transitions from red through yellow 
into green, from green through bluish-green and ultra- 
marine to violet, and from violet through purple to scarlet. 

Newton used the diagram of the colours of the spectrum 
(in a somewhat different form from that just given) 
only as a convenient way of representing the facts to 
the eye ; but recently Maxwell has succeeded in de- 
monstrating the strict and even quantitative accuracy 
of the principles involved in the construction of this 
diagram. His method is to produce combinations of 
colours on swiftly rotating discs, painted of various tints 
in sectors. When such a disc is turned rapidly round, 
so that the eye can no longer follow the separate hues, 
they melt into a uniform combination-colour, and the 
quantity of light which belongs to each can be directly 
measured by the breadth of the sector of the circle it 
occupies. Now the combination-colours which are pro- 
duced in this manner are exactly those which would result 
if the same qualities of coloured light illuminated the 
same surface continuously, as can be experimentally 
proved. Thus have the relations of size and number 
been introduced into the apparently inaccessible region 
of colours, and their differences in quality have been 
reduced to relations of quantity. 

All differences between colours may be reduced to three, 
which may be described as difference of tone, difference of 
fulness, or, as it is technically called, * saturation,' and 
difference of brightness. The differences of tone are those 
which exist between the several colours of the spectrum, 
and to which we give the names red, yellow, blue, violet, 
purple. Thus, with regard to tone, colours form a series 

1 The author has restored violet as a primitive colour in accordance with 
the experiments of J. J. Miiller, having in the first edition adopted the 
opinion of Maxwell that it is blue. 


which returns upon itself; a series which we complete 
when we allow the terminal colours of the rainbow to pass 
into one another through purple and crimson. It is in 
fact the same which we described as arranged around the 
circumference of the colour-disc. 

The fulness or saturation of colours is greatest in the 
pure tints of the spectrum, and becomes less in proportion 
as they are mixed with white light. This, at least, is 
true for colours produced by external light, but for our 
sensations it is possible to increase still further the 
apparent saturation of colour, as we shall presently see. 
Pink is a whitish-crimson, flesh-colour a whitish-scarlet, 
and so pale green, straw-colour, light blue, &c., are all 
produced by diluting the corresponding colours with 
white. All compound colours are, as a rule, less saturated 
than the simple tints of the spectrum. 

Lastly, we have the difference of brightness, or strength 
of light, which is not represented in the colour-disc. As 
long as we observe coloured rays of light, difference in 
brightness appears to be only one of quantity, not of quality. 
Black is only darkness that is", simple absence of light. 
But when \ve examine the colours of external objects^ black 
x^t5offesponds just as much to a peculiarity of surface in 
/ reflection, as does white, and therefore has as good a right 
to be called a colour. And as a matter of fact, we find 
in common language a series of terms to express colours 
with a small amount of light. We call them dark (or 
rather in English, deep) when they have little light but are 
6 full ' in tint, and grey when they are ' pale.' Thus dark 
blue conveys the idea of depth in tint, of a full blue with 
a small amount of light ; while grey-blue is a pale blue 
with a small amount of light. In the same way, the 
colours known as maroon, brown and olive are dark, 
more or less saturated tints of red, yellow and green re- 


In this way we may reduce all possible actual (ob- 
jective) differences in colour, so far as they are appre- 
ciated by the eye, to three kinds ; difference of hue (tone), 
difference of fulness (saturation), and difference of amount 
of illumination (brightness}. It is in this way that we de- 
scribe the system of colours in ordinary language. But we 
are able to express this threefold difference in another way. 

I said above that a properly constructed colour-disc 
approaches a triangle in its outline. Let us suppose for 
a moment that it is an exact rectilinear triangle, as made 
by the dotted line in Fig. 34 ; how far this differs from the 
actual condition we shall have afterwards to point out. 
Let the colours red, green, and violet be placed at the 
corners, then we see the law which was mentioned above : 
namely, that all the colours in the interior and on the 
sides of the triangle are compounds of the three at its 
corners. It follows that all differences of hue depend 
upon combinations in different proportions of the three 
primary colours. It is best to consider the three just 
named as primary ; the old ones red, yellow, and blue are 
inconvenient, and were only chosen from experience of 
painters' colours. It is impossible to make a green out 
of blue and yellow light. 

We shall better understand the remarkable fact that we 
are able to refer all the varieties in the composition of 
external light to mixtures of three primitive colours, if 
in this respect we compare the eye with the ear. 

Sound, as I mentioned before, is, like light, an undulat- 
ing movement, spreading by waves. In the case of sound 
also, we have to distinguish waves of various length which 
produce upon our ear impressions of different quality. 
We recognise the long waves as low notes, the short 
as high-pitched, and the ear may receive at once many 
waves of sound that is to say, many notes. But here 
these do not melt into compound notes, in the same waj 


that colours, when perceived at the same time and place, 
melt into compound colours. The eye cannot tell the 
difference, if we substitute orange for red and yellow ; but 
if we hear the notes C and E sounded at the same time, 
we cannot put D instead of them, without entirely 
changing the impression upon the ear. The most com- 
plicated harmony of a full orchestra becomes changed to 
our perception if we alter any one of its notes. No accord 
(or consonance of several tones) is, at least for the practised 
ear, completely like another, composed of different tones ; 
whereas, if the ear perceived musical tones as the eye 
colours, every accord might be completely represented by 
combining only three constant notes, one very low, one 
very high, and one intermediate, simply changing the 
relative strength of these three primary notes to produce 
all possible musical effects. 

In reality we find that an accord only remains un- 
changed to the ear, when the strength of each separate 
tone which it contains remains unchanged. Accordingly, if 
we wish to describe it exactly and completely, the strength 
of each of its component tones must be exactly stated. 

In the same way, the physical nature of a particular 
kind of light can only be fully ascertained by measuring 
and noting the amount of light of each of the simple 
colours which it contains. But in sunlight, in the light 
of most of the stars, and in flames, we find a continuous 
transition of colours into one another through numberless 
intermediate gradations. Accordingly, we must ascertain 
the amount of light of an infinite number of compound 
rays if we would arrive at an exact physical knowledge of 
sun or starlight. In the sensations of the eye we need 
distinguish for this purpose only the varying intensities 
of three components. 

The practised musician is able to catch the separate 
note? of the various instruments among the complicated 


harmonies of an entire orchestra, but the optician cannot 
directly ascertain the composition of light by means of 
the eye ; he must make use of the prism to decompose 
the light for him. As soon, however, as this is done, 
the composite character of light becomes apparent, and 
he can then distinguish the light of separate fixed stars 
from one another by the dark and bright lines which the 
spectrum shows him, and can recognise what chemical 
elements are contained in flames which are met with on 
the earth, or even in the intense heat of the sun's at- 
mosphere, in the fixed stars, or in the nebulae. The fact 
that light derived from each separate source carries with 
it certain permanent physical peculiarities is the founda- 
tion of spectral analysis that most brilliant discovery of 
recent years, which has opened the extreme limits of 
celestial space to chemical analysis. 

There is an extremely interesting and not very un- 
common defect of sight which is known as colour-blind- 
ness. In this condition the differences of colour are 
reduced to a still more simple system than that described 
above ; namely, to combinations of only two primary 
colours. Persons so affected are called colour-blind, 
because they confound certain hues which appear very 
different to ordinary eyes. At the same time they dis^- 
tinguish other colours, and that quite as accurately, or 
even (as it seems) rather more accurately, than ordinary 
people. They are usually ' red-blind ' ; that is to say, 
there is no red in their system of colours, and accordingly 
they see no difference which is produced by the addition 
of red. All tints are for them varieties of blue and green 
or, as they call it, yellow. Accordingly scarlet, flesh- 
colour, white, and bluish-green appear to them to be 
identical, or at the utmost to differ in brightness, The 
same applies to crimson, violet, and blue, and to red, 
orange, yellow, and green. The scarlet flowers of the 


geranium have for them exactly the same colours as its 
leaves. They cannot distinguish between the red and the 
green signals of trains. They cannot see the red end 
of the spectrum at all. Very full scarlet appears to them 
almost black, so that a red-blind Scotch clergyman went 
to buy scarlet cloth for his gown, thinking it was black. 1 

In this particular of discrimination of colours, we find 
remarkable inequalities in different parts Of the retina. 
In the first place all of us are red-blind in the outermost 
part of our field of vision. A geranium-blossom when 
moved backwards and forwards just within the field of 
sight, is only recognised as a moving object. Its colour 
is not seen, so that if it is waved in front of a mass 
of leaves of the same plant it cannot be distinguished 
from them in hue. In fact, all red colours appear much 
darker when viewed indirectly. This red-blind part of the 
retina is most extensive on the inner or nasal side of the 
field of vision ; and according to recent researches of 
Woinow, there is at the furthest limit of the visible field 
a narrow zone in which all distinction of colours ceases 
and there only remain differences of brightness. In this 
outermost circle everything appears white, grey, or black. 
Probably those nervous fibres which convey impressions 
of green light are alone present in this part of the retina. 

In the second place, as I have already mentioned, the 
middle of the retina, just around the central pit, is 
coloured yellow. This makes all blue light appear some- 
what darker in the centre of the field of sight. The 
effect is particularly striking with mixtures of red and 
greenish -blue, which appear white when looked at directly, 
but acquire a blue tint when viewed at a slight distance 

' A similar story is told of Dalton, the author of the 'Atomic Theory.' 
He was a Quaker, and went to 1he Friends' Meeting, at Manchester, in a 
pair of scarlet stockings, which some wag had put in place of his ordinary 
dark grey ones. TJR. 


from the middle of the field ; and, on the other hand, 
when they appear white here, are red to direct vision. 
These inequalities of the retina, like the others men- 
tioned in the former essay, are rectified by the con- 
stant movements of the eye. We know from the pale 
and indistinct colours of the external world as usually 
seen, what impressions of indirect vision correspond to 
those of direct ; and we thus learn to judge of the colours 
of objects according to the impression which they would 
make on us if seen directly. The result is, that only 
unusual combinations and unusual or special direction of 
attention enable us to recognise the difference of which I 
have been speaking. 

The theory of colours, with all these marvellous and 
complicated relations, was a riddle which Groethe in vain 
attempted to solve ; nor were we physicists and physio- 
logists more successful. I include myself in the number ; 
for I long toiled at the task, without getting any 
nearer my object, until I at last discovered that a 
wonderfully simple solution had been discovered at the 
beginning of this century, and had been in print ever 
since for any one to read who chose. This solution was 
found and published by the same Thomas Young * who 
first showed the right method of arriving at the in- 
terpretation of Egyptian hieroglyphics. He was one 
of the most acute men who ever lived, but had the 
misfortune to be too far in advance of his contempo- 
raries. They looked on him with astonishment, but could 
not follow his bold speculations, and thus a mass of his 
most important thoughts remained buried and forgotten 
in the ' Transactions of the Eoyal Society,' until a later 
generation by slow degrees arrived at the rediscovery of 
his discoveries, and came to appreciate the force of hia 
arguments and the accuracy of his conclusions. 

1 Born at Milverton, in Somersetshire, 1773, died 1829. 


In proceeding to explain the theory of colours proposed 
by him, I beg the reader to notice that the conclusions 
afterwards to be drawn upon the nature of the sensations 
of sight are quite independent of what is hypothetical in 
this theory. 

Dr. Young supposes that there are in the eye three 
kinds of nerve-fibres, the first of which, when irritated in 
any way, produces the sensation of red, the second the 
sensation of green, and the third that of violet. He 
further assumes that the first are excited most strongly 
by the waves of ether of greatest length ; the second, 
which are sensitive to green light, by the waves of middle 
length ; while those which convey impressions of violet 
are acted upon only by the shortest vibrations of ether. 
Accordingly, at the red end of the spectrum the excita- 
tion of those fibres which are sensitive to that colour pre- 
dominates ; hence the appearance of this part as red. 
Further on there is added an impression upon the fibres 
sensitive to green light, and thus results the mixed sensa- 
tion of yellow. In the middle of the spectrum, the nerves 
sensitive to green become much more excited than the 
other two kinds, and accordingly green is the predominant 
impression. As soon as this becomes mixed with violet 
the result is the colour known as blue ; while at the most 
highly refracted end of the spectrum the impression pro- 
duced on the fibres which are sensitive to violet light 
overcomes every other. 1 

It will be seen that this hypothesis is nothing more 
than a further extension of Johannes Miiller's law of special 

1 The precise tint of the three primary colours cannot yet be precisely 
ascertained by experiment. The red alone, it is certain from the experience 
of the colour-blind, belongs to the extreme red of the spectrum. At the 
other end Young took violet for the primitive colour, while Maxwell con- 
siders that it is more properly blue. The question is still an open one : 
according to J. J. Miiller's experiments (Archivfur Ophthalmologie, XV. 
2. p. 208) violet is more probable. The fluorescence of the retina is here 
a source of difficulty. 


sensation. Just as the difference of sensation of light and 
warmth depends demonstrably upon whether the rays of 
the sun fall upon nerves of sight or nerves of feeling, so 
it is supposed in Young's hypothesis that the difference 
of sensation of colours depends simply upon whether one 
or the other kind of nervous fibres are more strongly 
affected. When all three kinds are equally excited, the 
result is the sensation of white light. 

The phenomena that occur in red-blindness must be 
referred to a condition in which the one kind of nerves, 
which are sensitive to red rays, are incapable of excita- 
tion. It is possible that this class of fibres are wanting, 
or at least very sparingly distributed, along the edge .of 
the retina, even in the normal human eye. 

It must be confessed that both in men and in quadru 1 - 
peds we have at present no anatomical basis for this 
theory of colours ; but Max Schultze has discovered a struc- 
ture in birds and reptiles which manifestly corresponds 
with what we should expect to find. In the eyes of many 
of this group of animals there are found among the rods 
of the retina a number which contain a red drop of oil in 
their anterior end, that namely which is turned towards 
the light ; while other rods contain a yellow drop, and 
others none at all. Now there can be no doubt that red 
light will reach the rods with a red drop much better 
than light of any other colour, while yellow and green 
light, on the contrary, will find easiest entrance to the 
rods with the yellow drop. Blue light would be shut off 
almost completely from both, but would affect the colour- 
less rods all the more effectually. We may therefore with 
great probability regard these rods as the terminal organs 
of those nervous fibres which respectively convey impres- 
ions of red, of yellow, and of blue light. 

I have myself subsequently found a similar hypothesis 
convenient and well fitted to explain in a most 


simple manner certain peculiarities which have been 
observed in the perception of musical notes, peculiarities 
as enigmatical as those we have been considering in 
the eye. In the cochlea of the internal ear the ends 
of the nerve fibres lie regularly spread out side by side, 
and provided with minute elastic appendages (the rods 
of Corti) arranged like the keys and hammers of a piano. 
My hypothesis is, that here each separate nerve fibre is 
constructed so as to take cognizance of a definite note, to 
which its elastic fibre vibrates in perfect consonance. 
This is not the place to describe the special characters of 
our sensations of musical tones which led me to frame 
this hypothesis. Its analogy with Young's theory of 
colours is obvious, and it refers the origin of overtones, 
the perception of the quality of sounds, the difference 
between consonance and dissonance, the formation of the 
musical scale and other acoustic phenomena to as sim- 
ple a principle as that of Young. But in the case 
of the ear, I could point to a much more distinct 
anatomical foundation for such a hypothesis, and since 
that time, I have been able actually to demonstrate the 
relation supposed ; not, it is true, in man or any verte- 
brate animals, whose labyrinth lies too deep for experi- 
ment, but in some of the marine Crustacea. These animals 
have external appendages to their organs of hearing 
which may be observed in the living animal, jointed fila- 
ments to which the fibres of the auditory nerve are dis- 
tributed ; and Hensen, of Kiel, has satisfied himself that 
some of these filaments are set in motion by certain notes, 
and others by different ones. 

It remains to reply to an objection against Young's 
theory of colour. I mentioned above that the outline of 
the colour-disc, which marks the position of the most 
saturated colours (those of the spectrum), approaches to a 
triangle in form ; but our conclusions upon the theory of 


the three primary colours depend upon a perfect rectilinear 
triangle inclosing* the complete colour-system, for only in 
that case is it possible to produce all possible tints by 
various combinations of the three primary colours at the 
angles. It must, however, be remembered that the 
colour-disc only includes the entire series of colours 
which actually occur in nature, while our theory has to 
do with the analysis of our subjective sensations of colour. 
We need then only assume that actual coloured light does 
not produce sensations of absolutely pure colour ; that 
red, for instance, even when completely freed from all ad- 
mixture of white light, still does not excite those nervous 
fibres alone which are sensitive to impressions of red, but 
also, to a very slight degree, those which are sensitive to 
green, and perhaps to a still smaller extent those which 
are sensitive to violet rays. If this be so, then the sen- 
sation which the purest red light produces in the eye is 
still not the purest sensation of red which we can con- 
ceive of as possible. This sensation could only be called 
forth by a fuller, purer, more saturated red than has ever 
been seen in this world. 

It is possible to verify this conclusion. We are able 
to produce artificially a sensation of the kind I have vle- 
scribed. This fact is not only important as a complete 
answer to a possible objection to Young's theory, but is 
also, as will readily be seen, of the greatest importance 
for understanding the real value of our sensations of 
colour. In order to describe the experiment I must first 
give an account of a new series of phenomena. 

The result of nervous action is fatigue, and this will be 
proportioned to the activity of the function performed, 
and the time of its continuance. The blood, on the other 
hand, which flows in through the arteries, is constantly 
performing its function, replacing used material by fresh, 
and thus carrying away the chemical results of func- 


tional activity; that is to say, removing the source of 

The process of fatigue as the result of nervous action, 
takes place in the eye as well as other organs. When the 
entire retina becomes tired, as when we spend some time 
in the open air in brilliant sunshine, it becomes insensible 
to weaker light, so that if we pass immediately into a 
dimly lighted room we see nothing at first ; we are blinded, 
as we call it, by the previous brightness. After a time 
the eye recovers itself, and at last we are able to see, and 
even to read, by the same dim light which at first ap- 
peared complete darkness. 

It is thus that fatigue of the entire retina shows itself. 
But it is possible for separate parts of that membrane to 
become exhausted, if they alone have received a strong 
light. If we look steadily for some time at any bright 
object, surrounded by a dark background it is necessary 
to look steadily in order that the image may remain quiet 
upon the retina, and thus fatigue a sharply defined por- 
tion of its surface and afterwards turn our eyes upon a 
uniform dark -grey surface, we see projected upon it an 
after-image of the bright object we were looking at just 
before, with the same outline but with reversed illumina- 
tion. What was dark appears bright, and what was 
bright dark, like the first negative of a photographer. By 
carefully fixing the attention, it is possible to produce 
very elaborate after-images, so much so that occasionally 
even printing can be distinguished in them. This phe- 
nomenon is the result of a local fatigue of the retina. 
Those parts of the membrane upon which the bright light 
fell before, are now less sensitive to the light of the dark- 
grey background than the neighbouring regions, and 
there now appears a dark spot upon the really uniform 
surface, corresponding in extent to the surface of the 
retina which before received the bright light. 


(I may here remark that illuminated sheets of white 
paper are sufficiently bright to produce this after-image. 
If we look at much brighter objects at flames, or at the 
sun itself the effect becomes complicated. The strong 
excitement of the retina does not pass away immediately, 
but produces a direct or positive after-image, which at 
first unites with the negative or indirect one pioduced by 
the fatigue of the retina. Besides this, the effects of the 
different colours of white light differ both in duration and 
intensity, so that the after-images become coloured, and 
the whole phenomenon much more complicated.) 

By means of these after-images it is easy to convince 
oneself that the impression produced by a bright surface 
begins to diminish after the first second, and that by the 
end of a single minute it has lost from a quarter to half 
of its intensity. The simplest form of experiment for 
this object is as follows. Cover half of a white sheet of 
paper with a black one, fix the eye upon some point of 
the white sheet near the margin of the black, and after 
30 to 60 seconds draw the black sheet quickly away, 
without losing sight of the point. The half of the white 
sheet which is then exposed appears suddenly of the most 
brilliant brightness ; and thus it becomes apparent how 
very much the first impression produced by the upper half 
of the sheet had become blunted and weakened, even in 
the short time taken by the experiment. And yet, what 
is also important to remark, the observer does not at all 
notice this fact, until the contrast brings it before him. 

Lastly, it is possible to produce a partial fatigue of the 
retina in another way. We may tire it for certain colours 
only, by exposing either the entire retina, or a portion of 
it, for a certain time (from half a minute to five minutes) 
to one and the same colour. According to Young's theory, 
only one or two kinds of the optic nerve fibres will then 
be fatigued, those namely which are sensitive to impres* 


sions of the colour in question. All the rest will remain 
unaffected. The result is, that when the after-image 
appears, red, we will suppose, upon a grey background, 
the uniformly mixed light of the latter can only produce 
sensations of green and violet in the part of the retina 
which has become fatigued by red light. This part is 
made red-blind for the time. The after-image accord- 
ingly appears of a bluish green, the complementary colour 
to red. 

It is by this means that we are able to produce in 
the retina the pure and primitive sensations of satu- 
rated colours. If, for instance, we wish to see pure red, 
we fatigue a part of our retina by the bluish green of 
the spectrum, which is the complementary colour of 
red. We thus make this part at once green-blind and 
violet-blind. We then throw the after-image upon the 
red of as perfect a prismatic spectrum as possible ; the 
image immediately appears in full and burning red, while 
the red light, of the spectrum which surrounds it, although 
the purest that the world can offer, now seems to the un- 
fatigued part of the retina, less saturated than the after- 
image, and looks as if it were covered by a whitish mist. 

These facts are perhaps enough. I will not accumu- 
late further details, to understand which it would be 
necessary to enter upon lengthy descriptions of many 
separate experiments. 

We have already seen enough to answer the question 
whether it is possible to maintain the natural and innate 
conviction that the quality of our sensations, and espe- 
cially our sensations of sight, give us a true impression of 
corresponding qualities in the outer world. It is clear 
that they do not. The question was really decided by 
Johannes Miiller's deduction from well ascertained facts 
of the la of specific nervous energy. Whether the rays 


of the sun appear to us as colour, or as warmth, does not 
at all depend upon their own properties, but simply upon 
whether they excite the fibres of the optic nerve, or those 
of the skin. Pressure upon the eyeball, a feeble current 
of electricity passed through it, a narcotic drug carried to 
the retina by the blood, are capable of exciting the sen- 
sation of light just as well as the sunbeams. The most 
complete difference offered by our several sensations, that 
namely between those of sight, of hearing, of taste, of 
smell, and of touch this deepest of all distinctions, so 
deep that it is impossible to draw any comparison of like- 
ness, or unlikeness, between the sensations of colour 
and of musical tones does not, as we now see, at all de- 
pend upon the nature of the external object, but solely 
upon the central connections of the nerves which are 

We now see that the question whether within the 
special range of each particular sense it is possible to 
discover a coincidence between its objects and the sen- 
sations they produce is of only subordinate interest. 
What colour the waves of ether shall appear to us when 
they are perceived by the optic nerve depends upon their 
length. The system of naturally visible colours offers us 
a series of varieties in the composition of light, but the 
number of those varieties is wonderfully reduced from an 
unlimited number to only three. Inasmuch as the most 
important property of the eye is its minute appreciation 
of locality, and as it is so much more perfectly organised 
for this purpose than the ear, we may be well content 
that it is capable of recognising comparatively few 
differences in quality of light ; the ear, which in the 
latter respect is so enormously better provided, has scarcely 
any power of appreciating differences of locality. But 
it is certainly matter for astonishment to any one who 


trusts to the direct information of his natural senses, that 
neither the limits within which the spectrum affects our 
eyes, nor the differences of colour which alone remain 
as the simplified effect of all the actual differences of 
light in kind, should have any other demonstrable import 
than for the sense of sight. Light which is precisely the 
same to our eyes, may in all other physical and chemical 
effects be completely different. Lastly, we find that the 
unmixed primitive elements of all our sensations of 
colour (the perception of the simple primary tints) can- 
not be produced by any kind of external light in the 
natural unfatigued condition of the eye. These ele- 
mentary sensations of colour can only be called forth by 
artificial preparation of the organ, so that, in fact, 
they only exist as subjective phenomena. We see, there- 
fore, that as to any correspondence in kind of exter- 
nal light with the sensations it produces, there is only 
one bond of connection between them, a bond which at 
first sight may seem slender enough, but is in fact quite 
sufficient to lead to an infinite number of most useful 
applications. This law of correspondence between what 
is subjective and objective in vision is as follows: 

Similar light produces under like conditions a like 
sensation of colour. Light which under like conditions 
excites unlike sensations of colour is dissimilar. 

When two relations correspond to one another in this 
manner, the one is a sign for the other. Hitherto the 
notions of a ' sign' and of an ' image ' or representation have 
not been carefully enough distinguished in the theory of 
perception ; and this seems to me to have been the source 
of numberless mistakes and false hypotheses. In an 
' image ' the representation must be of the same kind as 
that which is represented. Indeed, it is only so far an 
image as it is like in kind. A statue is an image of 
a man, so far as its form reproduces his : even if it is 


executed on a smaller scale, every dimension will be 
represented in proportion. A picture is an image or 
representation of the original, first because it represents 
the colours of the latter by similar colours, secondly be- 
cause it represents a part of its relations in space those, 
namely, which belong to perspective by corresponding 
relations in space. 

Functional cerebral activity and the mental conceptions 
which go with it may be ' images ' of actual occurrences 
in the outer world, so far as the former represent the 
sequence in time of the latter, so far as they represent 
likeness of objects by likeness of signs that is, a regular 
arrangement by a regular arrangement. 

This is obviously sufficient to enable the understanding 
to deduce what is constant from the varied changes of 
the external world, and to formulate it as a notion or a 
law. That it is also sufficient for all practical purposes 
we shall see in the next chapter. But not only un- 
educated persons, who are accustomed to trust blindly to 
their senses, even the educated, who know that their 
senses may be deceived, are inclined to demur to so com- 
plete a want of any closer correspondence in kind between 
actual objects and the sensations they produce than the 
law I have just expounded. For instance, natural philo- 
sophers long hesitated to admit the identity of the rays 
of light and of heat, and exhausted all possible means of 
escaping a conclusion which seemed to contradict the 
evidence of their senses. 

Another example is that of Groethe, as I have en- 
deavoured to show elsewhere. He was led to contradict 
Newton's theory of colours, because he could not persuade 
himself that white, which appears to our sensation as the 
purest manifestation of the brightest light, could be com- 
posed of darker colours. It was Newton's discovery of 


the composition of light that was the first germ of the 
modern doctrine of the true functions of the senses ; and 
in the writings of his contemporary, Locke, were correctly 
laid down the most important principles on which the 
right interpretation of sensible qualities depends. But, 
however clearly we may feel that here lies the difficulty 
for a large number of people, I have never found the 
opposite conviction of certainty derived from the senses 
so distinctly expressed that it is possible to lay hold of 
the point of error ; and the reason seems to me to lie in 
the fact that beneath the popular notions on the subject 
lie other and more fundamentally erroneous concep- 

We must not be led astray by confounding the notions 
of a phenomenon and an appearance. The colours of 
objects are phenomena caused by certain real differences 
in their constitution. They are. according to the scientific 
as well as to the uninstructed view, no mere appearance, 
even though the way in which they appear depends chiefly 
upon the constitution of our nervous system. A ' decep- 
tive appearance ' is the result of the normal phenomena 
of one object being confounded with those of another. 
But the sensation of colour is by no means deceptive 
appearance. There is no other way in which colour 
can appear ; so that there is nothing which we could 
describe as the normal phenomenon, in distinction 
from the impressions of colour received through the 

Here the principal difficulty seems to me to lie in the 
notion of quality. All difficulty vanishes as soon as we 
clearly understand that each quality or property of a thing 
is, in reality, nothing else but its capability of exercising 
certain effects upon other things. These actions either 
go on between similar parts of the same body, and so 
produce the differences of its aggregate condition ; or 


they proceed from one body upon another, as in the case 
of chemical reactions ; or they produce their effect on our 
organs of special sense, and are there recognised as sensa- 
tions^ as those of sight, with which we have now to do. 
Any of these actions is called a ' property,' when its 
object is understood without being expressly mentioned. 
Thus, when we speak of the ' solubility ' of a substance, 
we mean its behaviour toward water ; when we speak of 
its 4 weight,' we mean its attraction to the earth ; and in 
the same way we may correctly call a substance ' blue,' 
understanding, as a tacit assumption, that we are only 
speaking of its action upon a normal eye. 

But if what we call a property always implies an action 
of one thing on another, then a property or quality can 
never depend upon the nature of one agent alone, but 
exists only in relation to, and dependent on, the nature 
of some second object, which is acted upon. Hence, 
there is really no meaning in talking of properties of 
light which belong to it absolutely, independent of all 
other objects, and which we may expect to find repre- 
sented in the sensations of the human eye. The notion 
of such properties is a contradiction in itself. They 
cannot possibly exist, and therefore we cannot expect to 
find any coincidence of our sensations of colour with 
qualities of light. 

These considerations have naturally long ago sug- 
gested themselves to thoughtful minds ; they may be 
found clearly expressed in the writings of Locke and 
Herbart, 1 and they are completely in accordance with 
Kant's philosophy. But in former times, they demanded 
a more than usual power of abstraction, in order that 
their truth should be understood ; whereas now the facts 

1 Johann Friedrich Herbart, born 1776, died 1841, professor of philo- 
sophy at Konigsberg and Gottingen, author of Psychologic als Wissen* 
ichaft, nevgegrundet auf Erfahrung, MctaphysiJc und Mathematik. TK. 


which we have laid before the reader illustrate them in 
the clearest manner. 

After this excursion into the world of abstract ideas, 
we return once more to the subject of colour, and will 
now examine it as a sensible ' sign ' of certain external 
qualities, either of light itself or of the objects which 
reflect it. 

It is essential for a good sign to be constant that is, 
the same sign must always denote the same object. Now, 
we have already seen that in this particular our sensations 
of colour are imperfect ; they are not quite uniform over 
the entire field of the retina. But the constant move- 
ment of the eye supplies this imperfection, in the same 
way as it makes up for the unequal sensitiveness of the 
different parts of the retina to form. 

We have also seen that when the retina becomes tired, 
the intensity of the impression produced on it rapidly 
diminishes, but here again the usual effect of the constant 
movements of the eye is to equalise the fatigue of the 
various parts, and hence we rarely see after-images. If 
they appear at all, it is in the case of brilliant objects like 
very bright flames, or the sun itself. And, so long as the 
fatigue of the entire retina is uniform, the relative 
brightness and colour of the different objects in sight 
remains almost unchanged, so that the effect of fatigue 
is gradually to weaken the apparent illumination of the 
entire field of vision. 

This brings us to consider the differences in the pictures 
presented by the eye, which depend on different degrees 
of illumination. Here again we meet with instructive 
facts. We look at external objects under light of very 
different intensity, varying from the most dazzling sun- 
shine to the pale beams of the moon ; and the light of 
the full moon is 150,000 times less than that of the sun. 


Moreover, the colour of the illumination may vary 
greatly. Thus, we sometimes employ artificial light, and 
this is always more or less orange in colour ; or the 
natural daylight is altered, as we see it in the green shade 
of an arbour, or in a room with coloured carpets and 
curtains. As the brightness and the colour of the illu- 
mination changes, so of course will the brightness and 
colour of the light which the illuminated objects reflect 
to our eyes, since all differences in local colour depend 
upon different bodies reflecting and absorbing various 
proportions of the several rays of the sun. Cinnabar 
reflects the rays of great wave length without any obvious 
loss, while it absorbs almost the whole of the other rays. 
Accordingly, this substance appears of the same red colour 
as the beams which it throws back into the eye. If it is 
illuminated with light of some other colour, without any 
mixture of red, it appears almost black. 

These observations teach what we find confirmed by 
daily experience in a hundred ways, that the apparent 
colour and brightness of illuminated objects varies with 
the colour and brightness of the illumination. This is a 
fact of the first importance for the painter, for many of 
his finest effects depend on it. 

But what is most important practically is for us to be 
able to recognise surrounding objects when we see them : 
it is only seldom that, for some artistic or scientific pur- 
pose, we turn our attention to the way in which they are 
illuminated. Now what is constant in the colour of an 
object is not the brightness and colour of the light which 
it reflects, but the relation between the intensity of the 
different coloured constituents of this light, on the one 
hand, and that of the corresponding constituents of the 
light which illuminates it on the other. This proportion 
alone is the expression of a constant property of the 
object in question. 


Considered theoretically, the task of judging of the 
colour of a body under changing illumination would seem 
to be impossible ; but in practice we soon find that we 
are able to judge of local colour without the least un- 
certainty or hesitation, and under the most different 
conditions. For instance, white paper in full moonlight 
is darker than black satin in daylight, but we never find 
any difficulty in recognising the paper as white and the 
satin as black. Indeed, it is much more difficult to 
satisfy ourselves that a dark object with the sun shining 
on it reflects light of exactly the same colour, and 
perhaps the same brightness, as a white object in sha- 
dow, than that the proper colour of a white paper in 
shadow is the same as that of a sl:eet of the same kind 
lying close to it in the sunlight. Grey seems to us 
something altogether different from white, and so it is. 
regarded as a proper colour ; l for anything which only 
reflects half the light it receives must have a different 
surface from one which reflects it all. And yet the im- 
pression upon the retina of a grey surface under illumi- 
nation may be absolutely identical with that of a white 
surface in the shade. Every painter represents a white 
object in shadow by means of grey pigment, and if he 
has correctly imitated nature, it appears pure white. In 
order to convince one's self of the identity in this respect 
i.e. as illumination colours of grey and white, the 
following experiment may be tried. Cut out a circle in 
grey paper, and concentrate a strong beam of light upon 
it with a lens, so that the limits of the illumination 
exactly correspond with those of the grey circle. It will 

1 The local or proper colour of an object (Kbrperfarbe) is that which it 
shows in common white light, while the ' illumination-colour,' as I have 
translated Lichtfarbe, is that which is produced by coloured light. Thus 
the red of some sandstone rocks seen by common white light is their proper 
colour, that of a snow mountain in the rays of the setting sun is an illu 
mination-colour. TB. 


then be impossible to tell that there is any artificial il- 
lumination at all. The grey looks white. 1 

We may assume, and the assumption is justified by 
certain phenomena of contrast, that illumination of the 
brightest white we can produce, gives a true criterion for 
judging of the darker objects in the neighbourhood, since, 
under ordinary circumstances, the brightness of any proper 
colour diminishes in proportion as the illumination is 
diminished, or the fatigue of the retina increased. 

This relation holds even for extreme degrees of illu- 
mination, so far as the objective intensity of the light is 
concerned, but not for our sensation. Under illumination 
so brilliant as to approach what would be blinding, degrees 
of brightness of light-coloured objects become less and 
less distinguishable ; and, in the same way, when the 
illumination is very feeble, we are unable to appreciate 
slight differences in the amount of light reflected by dark 
objects. The result is that in sunshine local colours of 
moderate brightness approach the brightest, whereas in 
moonlight they approach the darkest. The painter utilises 
this difference in order to represent noonday or midnight 
scenes, although pictures, which are usually seen in uni- 
form daylight, do not really admit of any difference of 
brightness approaching that between sunshine and moon- 
light. To represent the former, he paints the objects of 
moderate brightness almost as bright as the brightest ; for 
the latter, he makes them almost as dark as the darkest. 

The effect is assisted by another difference in the sen- 
sation produced by the same actual conditions of light and 
colour. If the brightness of various colours is equally in- 
creased, that of red and yellow becomes apparently stronger 
than that of blue. Thus, if we select a red and a blue paper 
which appear of the same brightness in ordinary daylight, 

1 The demonstration is more striking if the grey disk is placed on a sheet 
of white paper in diffused light. TB. 


the red seems much brighter in full sunlight, the blue in 
moonlight or starlight. This peculiarity in our perception 
is also made use of by painters ; they make yellow tints 
predominate when representing landscapes in full sun- 
shine, while every object of a moonlight scene is given a 
shade of blue. But it is not only local colour which is 
thus affected ; the same is true of the colours of the 

These examples show very plainly how independent our 
judgment of colours is of their actual amount of illu- 
mination. In the same way, it is scarcely affected by the 
colour of the illumination. We know, of course, in a 
general way that candle-light is yellowish compared with 
daylight, but we only learn to appreciate how much the 
two kinds of illumination differ in colour when we bring 
them together of the same intensity as, for example, in 
the experiment of coloured shadows. If we admit light 
from a cloudy sky through a narrow opening into a dark 
room, so that it falls sideways on a horizontal sheet of 
white paper, while candle-light falls on it from the other 
side, and if we then hold a pencil vertically upon the 
paper, it will of course throw two shadows : the one made 
by the daylight will be orange, and looks so ; the other 
made by the candle-light is really white, but appears blue 
by contrast. The blue and the orange of the two shadows 
are both colours which we call white, when we see them 
by daylight and candle-light respectively. Seen to- 
gether, they appear as two very different and tolerably 
saturated colours, yet we do not hesitate a moment in 
recognising white paper by candle-light as white, and 
very different from orange. 1 

The most remarkable of this series of facts is that we 
can separate the colour of any transparent medium from 

1 This experiment with diffused white day-light may also be made witl 


that of objects seen through it. This is proved by a 
number of experiments contrived to illustrate the effects 
of contrast. If we look through a green veil at a field of 
snow, although the light reflected from it must really 
have a greenish tint when it reaches our eyes, yet it 
appears, on the contrary, of a reddish tint, from the effect 
of the indirect after-image of green. So completely 
are we able to separate the light which belongs to the 
transparent medium from that of the objects seen 
through it. 1 

The changes of colour in the two last experiments are 
known as phenomena of contrast. They consist in mis- 
takes as to local colour, which for the most part depend 
upon imperfectly defined after-images. 2 This effect is 
known as successive contrast, and is experienced when the 
eye passes over a series of coloured objects. But a similar 
mistake may result from our custom of judging of local 
colour according to the brightness and colour of the 
various objects seen at the same time. If these relations 
happen to be different from what is usual, contrast phe- 
nomena ensue. When, for example, objects are seen 
under two different coloured illuminations, or through 
two different coloured media (whether real or apparent), 
these conditions produce what is called simultaneous 
contrast. Thus in the experiment described above of 
coloured shadows thrown by daylight and candle-light, 
the doubly illuminated surface of the paper being the 
brightest object seen, gives a false criterion for white. Com- 
pared with it, the really white but less bright light of the 
shadow thrown by the candle looks blue. Moreover, in 
these curious effects of contrast, we must take into account 

1 A number of similar experiments will be found described in the 
author's Handbuch der physiologischen Optik, pp. 398-411. 

2 These after-images have been described as ' accidental images,' positive 
when of the same colour as the original colour, negative when of the com* 
plementary colour. TK. 


that differences in sensation which are easily appre- 
hended appear to us greater than those less obvious. 
Differences of colour which are actually before our eyes 
are more easily apprehended than those which we only 
keep in memory, and contrasts between objects which are 
close to one another in the field of vision are more easily 
recognised than when they are at a distance. All this 
contributes to the effect. Indeed, there are a number of 
subordinate circumstances affecting the result which it 
would be very interesting to follow out in detail, for they 
throw great light upon the way in which we judge of 
local colour : but we must not pursue the inquiry further 
here. I will only remark that all these effects of contrast 
are not less interesting for the scientific painter than for 
the physiologist, since he must often exaggerate the 
natural phenomena of contrast, in order to produce the 
impression of greater varieties of light and greater fulness 
of colour than can be actually produced by artificial 

Here we must leave the theory of the Sensations of 
Sight. This part of our inquiry has shown us that the 
qualities of these sensations can only be regarded as signs 
of certain different qualities, which belong sometimes to 
light itself, sometimes to the bodies it illuminates, but 
that there is not a single actual quality of the objects 
seen which precisely corresponds to our sensations of sight. 
Nay, we have seen that, even regarded as signs of real 
phenomena in the outer world, they do not possess the 
one essential requisite of a complete system of signs 
namely, constancy with anything like completeness ; so 
that all that we can say of our sensations of sight is, 
that ' under similar conditions, the qualities of this sen- 
sation appear in the same way for the same objects.' . 

And yet, in spite of all this imperfection, we have also 


found that by means of so inconstant a system of signs, 
we are able to accomplish the most important part of our 
task to recognise the same proper colours wherever they 
occur ; and, considering the difficulties in the way, it is 
surprising how well we succeed. Out of this inconstant 
system of brightness and of colours, varying according to 
the illumination, varying according to the fatigue of the 
retina, varying according to the part of it affected, we are 
able to determine the proper colour of any object, the one 
constant phenomenon which corresponds to a constant 
quality of its surface ; and this we can do, not after long 
consideration, but by an instantaneous and involuntary 

The inaccuracies and imperfections of the eye as an 
optical instrument, and those which belong to the image 
on the retina, now appear insignificant in comparison with 
the incongruities which we have met with in the field of 
sensation. One might almost believe that Nature had 
here contradicted herself on purpose, in order to destroy 
any dream of a pre-existing harmony between the outer 
and the inner world. 

And what progress have we made in our task of ex- 
plaining Sight ? It might seem that we are farther off 
than ever ; the riddle only more complicated, and less 
hope than ever of finding out the answer. The reader 
may perhaps feel inclined to reproach Science with only 
knowing how to break up with fruitless criticism the fair 
world presented to us by our senses, in order to annihi- 
late the fragments. 

Woe ! woe ! 

Thou hast destroyed 

The beautiful world 

With powerful fist ; 

In ruin 'tis hurled, 

By the blow of a demigod shattered. 


The scattered 

Fragments into the void we carry, 


The beauty perished beyond restoring. 1 

and may feel determined to stick fast to the c sound com- 
mon sense ' of mankind, and believe his own senses more 
than physiology. 

But there is still a part of our investigation which we 
have not touched that into our conceptions of space. 
Let us see whether, after all, our natural reliance upon the 
accuracy of what our senses teach us, will not be justified 
even before the tribunal of Science. 


The colours which have been the subject of the last 
chapter are not only an ornament we should be sorry to 
lose, but are also a means of assisting us in the distinction 
and recognition of external objects. But the importance 
of colour for this purpose is far less than the means which 
the rapid and far-reaching power of the eye gives us of 
distinguishing the various relations of locality. No other 
sense can be compared with the eye in this respect. The 
sense of touch, it is true, can distinguish relations of 
Bpace, and has the special power of judging of all matter 

1 Bayard Taylor s translation of the passage in Faust : 

Du hast sie zerstort 

Die schone Welt 

Mit machtiger Faust ; 

Sie stiirzt, sie zerfallt, 

Ein Halbgott hat sie zerschlagen. 

Wir tragen 

Die Trummern ins Nichts hinuber, 

Und klagen 

Ueber die verlorne Sclioae. 


within reach, at once as to resistance, volume, and weight ; 
but the range of touch is limited, and the distinction it 
can make between small distances is not nearly so accu- 
rate as that of sight. Yet the sense of touch is sufficient, 
as experiments upon persons born blind have proved, to 
develop complete notions of space. This proves that the 
possession of sight is not necessary for the formation of 
these conceptions, and we shall soon see that we are con- 
tinually controlling and correcting the notions of locality 
derived from the eye by the help of the sense of touch, 
and always accept the impressions on the latter sense as 
decisive. The two senses, which really have the same 
task, though with very different means of accomplishing 
it, happily supply each other's deficiencies. Touch is a 
trustworthy and experienced servant, but enjoys only a 
limited range, while sight rivals the boldest nights of 
fancy in penetrating to illimitable distances. 

This combination of the two senses is of great im- 
portance for our present task; for, since we have here 
only to do with vision, and since touch is sufficient to 
produce complete conceptions of locality, we may assume 
these conceptions to be already complete, at least in their 
general outline, and may, accordingly, confine our in- 
vestigation to ascertaining the common point of agree- 
ment between the visual and tactile perceptions of space. 
The question how it is possible for any conception of 
locality to arise from either or both of these sensations, 
we will leave till last. 

It is obvious, from a consideration of well-known facts, 
that the distribution of our sensations among nervous 
structures separated from one another does not at all 
necessarily bring with it the conception that the causes of 
these sensations are locally separate. For example, we 
may have sensations of light, of warmth, of various notes 
of music, and also perhaps of an odour, in the same room, 


and may recognise that all these agents are diffused 
through the air of the room at the same time, and without 
any difference of locality. When a compound colour 
falls upon the retina, we are conscious of three separate 
elementary impressions, probably conveyed by separate 
nerves, without any power of distinguishing them. We 
hear in a note struck on a stringed instrument or in the 
human voice, different tones at the same time, one fun- 
damental, and a series of harmonic overtones, which also 
are probably received by different nerves, and yet we are 
unable to separate them in space. Many articles of food 
produce a different impression of taste upon different 
parts of the tongue, and also produce sensations of odour 
by their volatile particles ascending into the nostrils 
from behind. But these different sensations, recognised 
by different parts of the nervous system, are usually 
completely and inseparably united in the compound sen 
sation which we call taste. 

No doubt, with a little attention it is possible to 
ascertain the parts of the body which receive these sen- 
sations, but, even when these are known to be locally 
separate, it does not follow that we must conceive of the 
sources of these sensations as separated in the same 

We find a corresponding fact in the physiology of sight 
namely, that we see only a single object with our two 
eyes, although the impression is conveyed by two distinct 
nerves. In fact, both phenomena are examples of a more 
universal law. 

Hence, when we find that a plane optical image of the 
objects in the field of vision is produced on the retina, 
and that the different parts of this image excite different 
fibres of the optic nerve, this is not a sufficient ground 
for our referring the sensations thus produced to locally 
distinct regions of our field of vision. Something else 


mast clearly be added to produce the notion of separation 
in space. 

The sense of touch offers precisely the same problem. 
When two different parts of the skin are touched at the 
same time, two different sensitive nerves are excited, but 
the local separation between these two nerves is not a 
sufficient ground for our recognition of the two parts 
which have been touched as distinct, and for the concep- 
tion of two different external objects which follows. 
Indeed, this conception will vary according to circum- 
stances. If we touch the table with two fingers, and feel 
under each a grain of sand, we suppose that there are two 
separate grains of sand ; but if we place the two fingers 
one against the other, and a grain of sand between them, 
we may have the same sensations of touch in the same 
two nerves as before, and yet, under these circumstance?, 
we suppose that there is only a single grain. In this case, 
our consciousness of the position of the fingers has ob- 
viously an influence upon the result at which the mind 
arrives. This is further proved by the experiment of 
crossing two fingers one over the other, and putting a 
marble between them, when the single object will produce 
in the mind the conception of two. 

What, then, is it which comes to help the anatomical 
distinction in .locality between the different sensitive 
nerves, and, in cases like those I have mentioned, produces 
the notion of separation in space ? In attempting to 
answer this question, we cannot avoid a controversy which 
has not yet been decided. 

Some physiologists, following the lead of Johannes 
Miiller, would answer that the retina or skin, being itself 
an organ which is extended in space, perceives impressions 
which carry with them this quality of extension in space ; 


that this conception of locality is innate ; and that im- 
pressions derived from external objects are transmitted of 
themselves to corresponding local positions in the image 
produced in the sensitive organ. We may describe this as 
the Innate or Intuitive Theory of conceptions of Space. 
It obviously cuts short all further enquiry into the origin 
of these conceptions, since it regards them as some- 
thing original, inborn, and incapable of further explana- 

The opposing view was put forth in a more general 
form by the early English philosophers of the sensational 
school by Molyneux, 1 Locke, and Jurin. 2 Its applica- 
tion to special physiological problems has only become 
possible in very modern times, particularly since we have 
gained more accurate knowledge of the movements of the 
eye. The invention of the stereoscope by Wheatstone 
(p. 284) made the difficulties and imperfections of the 
Innate Theory of sight much more obvious than before, 
and led to another solution which approached much 
nearer to the older view, and which we will call the 
Empirical Theory of Vision. This assumes that none of 
our sensations give us anything more than ' signs ' for ex- 
ternal objects and movements, and that we can only learn 
how to interpret these signs by means of experience and 
practice. For example, the conception of differences in 
locality can only be attained by means of movement, and, 
in the field of vision, depends upon our experience of the 
movements of the eye. Of course, this Empirical Theory 
must assume a difference between the sensations of 
various parts of the retina, depending upon their local 

1 "William Molyneux, author of Dioptrica Nova, was born in Dublin, 1656, 
and died in the same city, 1698. 

2 James Jurin, M.D., Sec. R. S., physician to Guy's Hospital, and Presi- 
dent of the Royal College of Physicians, was born in 1684, and died in 1750. 
Beside works on the Contraction of the Heart, on Vis viva, &c., he pub- 
lished, in 1738, a treatise on Distinct and Indistinct Vision. TR. 


difference. If it were not so, it would be impossible to 
distinguish any local difference in the field of vision. The 
sensation of red, when it falls upon the right side of the 
retina, must in some way be different from the sensation 
of the same red when it affects the left side ; and, more- 
over, this difference between the two sensations must be 
of another kind from that which we recognise when the 
same spot in the retina is successively affected by two 
different shades of red. Lotze l has named this difference 
between the sensations which the same colour excites 
when it affects different parts of the retina, the local sign 
of the sensation. "We are for the present ignorant of the 
nature of this difference, but I adopt the name given by 
Lotze as a convenient expression. While it would be 
premature to form any further hypothesis as to the 
nature of these k local signs,' there can be no doubt 
of their existence, for it follows from the fact that we 
are able to distinguish local differences in the field of 

The difference, therefore, between the two opposing 
views is as follows. The Empirical Theory regards the 
local signs (whatever they really may be) as signs the 
signification of which must be learnt, and is actually 
learnt, in order to arrive at a knowledge of the external 
world. It is not at all necessary to suppose any kind of 
correspondence between these local signs and the actual 
differences of locality which they signify. The Innate 
Theory, on the other hand, supposes that the local signs 
are nothing else than direct conceptions of differences 
in space as such, both in their nature and their magni- 

1 Eudolf Hermann Lotze, Professor in the University of Gottingen, 
originally a disciple of Herbart (v. supra), author of Attgemeim Physiologie 
des menschlichen Korpers, 1851. TE. 



The reader will see how the subject of our present 
enquiry involves the consideration of that far-reaching 
opposition between the system of philosophy which as- 
sumes a pre-existing harmony of the laws of mental 
operations with those of the outer world, and the system 
which attempts to derive all correspondence between 
mind and matter from the results of experience. 

So long as we confine ourselves to the observation of a 
field of two dimensions, the individual parts of which 
offer no, or, at any rate, no recognisable, difference in 
their distances from the eye so long, for instance, as 
we only look at the sky and distant parts of the land- 
scape, both the above theories practically offer an equally 
good explanation of the way in which we form concep- 
tions of local relations in the field of vision. The extension 
of the retinal image corresponds to the extension of the 
actual image presented by the objects before us ; or, at 
all events, there are no incongruities which may not be 
reconciled with the Innate Theory of sight without any 
very difficult assumptions or explanations. 

The first of these incongruities is that in the retinal 
picture the top and bottom and the right and left of the 
actual image are inverted. This is seen in Fig. 30 to 
result from the rays of light crossing as they enter the 
pupil ; the point a is the retinal image of A, b of B. 
This has always been a difficulty in the theory of vision, 
and many hypotheses have been invented to explain it. 
Two of these have survived. \Ve may, with Johannes 
Miiller, regard the conception of upper and lower as only 
a relative distinction, so far as sight is concerned that 
is, as only affecting the relation of the one to the other ; 
and we must further suppose that the feeling of corre- 
spondence between what is upper in the sense of sight and 
in the sense of touch is only acquired by experience, 


when we see the hands, which feel, moving in the field of 
vision. Or, secondly, we may assume with Fick x that, 
since all impressions upon the retina must be conveyed to 
the brain in order to be there perceived, the nerves of 
sight and those of feeling are so arranged in the brain as 
to produce a correspondence between the notions they 
suggest of upper and under, right and left. This sup- 
position has, however, no pretence of any anatomical facts 
to support it. 

The second difficulty for the Intuitive Theory is that, 
while we have two retinal pictures, we do not see double. 
This difficulty was met by the assumption that both retinae 
when they are excited produce only a single sensation in 
the brain, and that the several points of each retina corre- 
spond with each other, so that each pair of corresponding or 
* identical ' points produces the sensation of a single one. 
Now there is an actual anatomical arrangement which 
might perhaps support this hypothesis. The two optic 
nerves cross before entering the brain, and thus become 
united. Pathological observations make it probable that 
the nerve-fibres from the right-hand halves of both retinas 
pass to the right cerebral hemisphere, those from the left 
halves to the left hemisphere. 2 But although correspond- 
ing nerve-fibres would thus be brought close together, it 
has not yet been shown that they actually unite in the 

1 Ludwig Fick, late Professor of Medicine in the University of Marburg, 
the brother of Prof. Adolf Fick, of Zurich. 

2 We may compare the arrangement to that of the reins of a pair of 
horses : the inner fibres only of each optic nerve cross, so that those which 
run to the right half of the brain are the outer fibres of the right and the 
inner of the left retina, while those which run to the left cerebral hemi- 
sphere are the outer fibres of the left and the inner of the right retina : 
just as the inner reins of both horses cross, so that the outer rein of the off 
horse and the inner of the near one run together to the driver's right hand, 
while the inner rein of the off and the outer of the near horse pass to his 
left hand. TE. 


These two difficulties do not apply to the Empirical 
Theory, since it only supposes that the actual sensible 
c sign,' whether it be simple or complex, is recognised as 
the sign of that which it signifies. An uninstructed 
person is as sure as possible of the notions he derives 
from his eyesight, without ever knowing that he has two 
retinae, that there is an inverted picture on each, or that 
there is such a thing as an optic nerve to be excited, or a 
brain to receive the impression. He is not troubled by 
his retinal images being inverted and double. He knows 
what impression such and such an object in such and 
such a position makes on him through his eyesight, 
and governs himself accordingly. But the possibility of 
learning the signification of the local signs which belong 
to our sensations of sight, so as to be able to recognise 
the actual relations which they denote, depends, first, on 
our having movable parts of our own body within sight ; 
so that, when we once know by means of touch what rela- 
tion in space and what movement is, we can further 
learn what changes in the impressions on the eye cor- 
respond to the voluntary movements of a hand which we 
can see. In the second place, when we move our eyes 
while looking at a field of vision filled with objects at 
rest, the retina, as it moves, changes its relation to the 
almost unchanged position of the retinal picture. We 
thus learn what impression the same object makes upon 
different parts of the retina. An unchanged retinal 
picture, passing over the retina as the eye turns, is like a 
pair of compasses which we move over a drawing in order 
to measure its parts. Even if the ' local signs ' of sensa- 
tion were quite arbitrary, thrown together without any 
systematic arrangement (a supposition which I regard as 
improbable), it would still be possible by means of the 
movements of the hand and of the eye, as just described, 


to ascertain which signs go together, and which correspond 
in different regions of the retina to points at similar 
distances in the two dimensions of the field of vision. 
This is in accordance with experiments by Fechner, 1 
Volkmann, 2 and myself, which prove that even the fully 
developed eye of an adult can only accurately compare 
the size of those lines or angles in the field of vision, the 
images of which can be thrown one after another upon 
precisely the same spot of the retina by means of the 
ordinary movements of the eye. 

Moreover, we may convince ourselves by a simple ex- 
periment that the harmonious results of the perceptions 
of feeling and of sight depend, even in the adult, upon a 
constant comparison of the two, by means of the retinal 
pictures of our hands as they move. If we put on a pair 
of spectacles with prismatic glasses, the two flat surfaces 
of which converge towards the right, all objects appear to 
be moved over to the right. If we now try to touch any- 
thing we see, taking care to shut the eyes before the hand 
appears in sight, it passes to the right of the object ; but 
if we follow the movement of the hand with the eye, we 
are able to touch what we intend, by bringing the retinal 
image of the hand up to that of the object. Again, if 
we handle the object for one or two minutes, watching 
it all the time, a fresh correspondence is formed between 
the eye and the hand, in spite of the deceptive glass, 
so that we are now able to touch the object with per- 
fect certainty, even when the eyes are shut. And we 
can even do the same with the other hand without seeing 
it, which proves that it is not the perception of touch 

1 Gustav Theodor Fechner, author of Elemcnte der PsychophysiJc, 1860 ; 
also known as a satirist. TR. 

2 Alfred Wilhelra Volkmann, successively Professor of Physiology at 
Leipzig, Dorpat, and Halle; author of Physiologische Untersuchungen im 
Gebiete der Optik, 1864, &c. TR. 


which has been rectified by comparison with the false 
retinal images, but, on the contrary, the perception of 
sight which has been corrected by that of touch. But, 
again, if, after trying this experiment several times, /we 
take off the spectacles and then look at any object, taking 
care not to bring our hands into the field of vision, and 
now try to touch it with our eyes shut, the hand will pass 
beyond it on the opposite side that is, to the left. The 
new harmony which was established between the percep- 
tions of sight and of touch continues its effects, and thus 
leads to fresh mistakes when the normal conditions are 

In preparing objects with needles under a compound 
microscope, we must learn to harmonise the inverted mi- 
croscopical image with our muscular sense ; and we have 
to get over a similar difficulty in shaving before a look- 
ing-glass, which changes right to left. 

These instances, in which the image presented in the 
two dimensions of the field of vision is essentially of the 
same kind as the retinal images, and resembles them, can 
be equally well explained (or nearly so) by the two oppo- 
site theories of vision to which I have referred. But it is 
quite another matter when we pass to the observation of 
near objects of three dimensions. In this case there is a 
thorough and compbte incongruity between our retinal 
images on the one hand, and, on the other, the actual 
condition of the objects as well as the correct impression 
of them which we receive. Here we are compelled to 
choose between the two opposite theories, and accordingly 
this department of our subject the explanation of our 
Perception of Solidity or Depth in the field of vision, and 
that of binocular vision on which the former chiefly 
depends has for many years become the field of much 
investigation and no little controversy. And no won- 


der, for we have already learned enough to see that the 
questions which have here to be decided are of funda- 
mental importance, not only for the physiology of sight, 
but for a correct understanding of the true nature and 
limits of human knowledge generally. 

Each of our eyes projects a plane image upon its own 
retina. However we may suppose the conducting nerves 
to be arranged, the two retinal images when united in 
the brain can only reappear as a plane image. But 
instead of the two plane retinal images, we find that 
the actual impression on our mind is a solid image of 
three dimensions. Here, again, as in the system of 
colours, the outer world is richer than our sensation by 
one dimension ; but in this case the conception formed 
by the mind completely represents the reality of the 
outer world. It is important to remember that this 
perception of depth is fully as vivid, direct, and exact 
as that of the plane dimensions of the field of vision. 
If a man takes a leap from one rock to another, his life 
depends just as much upon his rightly estimating the 
distance of the rock on which he is to alight, as upon 
his not misjudging its position, right or left; and, as 
a matter of experience, we find that we can do the one 
just as quickly and as surely as the other. 

In what way can this appreciation of what we call 
depth, solidity, and direct distance come about ? Let 
us first ascertain what are the facts. 

At the outset of the enquiry we must bear in mind 
that the perception of the solid form of objects and 
of their relative distance from us is not quite absent, 
even when we look at them with only one eye and 
without changing our position. Now the means which 
we possess in this case are just the same as those which 
*he painter can employ in order to give the figures on 
his canvas the appearance of being solid objects, and of 


standing at different distances from the spectator. It is 
part of a painter's merit for his figures to stand out 
boldly. Now how does he produce the illusion? We 
shall find, in the first place, that in painting a landscape 
he likes to have the sun near the horizon, which gives 
him strong shadows ; for these throw objects in the 
foreground into bold relief. Next he prefers an atmo- 
sphere which is not quite clear, because slight obscurity 
makes the distance appear far off. Then he is fond of 
bringing in figures of men and cattle, because, by help of 
these objects of known size, we can easily measure the 
size and distance of other parts of the scene. Lastly, 
houses and other regular productions of art are also 
useful for giving a clue to the meaning of the picture, 
since they enable us easily to recognise the position of 
horizontal surfaces. The representation of solid forms 
by drawings in correct perspective is most successful in 
the case of objects of regular and symmetrical shape, 
such as buildings, machines, and implements of various 
kinds. For we know that all of these are chiefly bounded 
either by planes which meet at a right angle or by 
spherical and cylindrical surfaces ; and this is sufficient 
to supply what the drawing does not directly show. 
Moreover, in the case of figures of men or animals, our 
knowledge that the two sides are symmetrical further 
assists the impression conveyed. 

But objects of unknown and irregular shape, as rocks 
or masses of ice, baffle the skill of the most consummate 
artist ; and even their representation in the most com- 
plete and perfect manner possible, by means of photo- 
graphy, often shows nothing but a confused mass of 
black and white. Yet, when we have these objects in 
reality before our eyes, a single glance is enough for 
us to recognise their form. 

The first \\ho clearly showed in what points it is 


impossible for any picture to represent actual objects was 
the great master of painting, Leonardo da Vinci, 1 who 
was almost as distinguished in natural philosophy as in 
art. He pointed out in his Trattato della Pittura^ that 
the views of the outer world presented by each of our 
eyes are not precisely the same. Each eye sees in its 
retinal image a perspective view of the objects which 
lie before it ; but, inasmuch as it occupies a somewhat 
different position in space from the other, its point 
of view and so its whole perspective image is dif- 
ferent. If I hold up my finger and look at it first 
with the right and then with the left eye, it covers, 
in the picture seen by the latter, a part of the opposite 
wall of the room which is more to the right than in 
the picture seen by the right eye. If I hold up my right 
hand with the thumb towards me, I see with the right 
eye more of the back of the hand, with the left more 
of the palm ; and the same effect is produced whenever 
we look at bodies of which the several parts are at 
different distances from our eyes. But when I look at a 
hand represented in the same position in a painting, the 
right eye will see exactly the same figure as the left, and 
just as much of either the palm or the back of it. Thus 
we see that actual solid objects present different pictures 
to the two eyes, while a painting shows only the same. 
Hence follows a difference in the impression made upon 
the sight which the utmost perfection in a representation 
on a flat surface cannot supply. 

The clearest proof that seeing with two eyes, and the 
difference of the pictures presented by each, constitute 

1 Born at Vinci, near Florence, 1452 ; died at Cloux, near Amboise, 1519. 
Mr. Hallam says of his scientific writings, that they are ' more like revela- 
tions of physical truths vouchsafed to a single mind, than the super- 
structure of its reasoning upon any established basis. ... He first laid 
down the grand principle of Bacon, that experiment and observation must 
be the guides to just theory in the investigation of nature.' Ta. 


the most important cause of our perception of a third 
dimension in the field of vision, has been furnished by 
Wheatstone's invention of the stereoscope. 1 I may assume 
that this instrument and the peculiar illusion which it 
produces are well known. By its help we see the solid 
shape of the objects represented on the stereoscopic 
slide, with the same complete evidence of the senses with 
which we should look at the real objects themselves. 
This illusion is produced by presenting somewhat dif- 
ferent pictures to the two eyes to the right, one which 
represents the object in perspective as it would appear 
to that eye, and to the left one as it would appear to the 
left. If the pictures are otherwise exact and drawn from 
two different points of view corresponding to the position 
of the two eyes, as can be easily done by photography, we 
receive on looking into the stereoscope precisely the same 
impression in black and white as the object itself would 

Anyone who has sufficient control over the movements 
of his eyes does not need the help of an instrument in 
order to combine the two pictures on a stereoscopic slide 
into a single solid image. It is only necessary so to 
direct the eyes, that each of them shall at the same time 
see corresponding points in the two pictures; but it is 
easier to do so by help of an instrument which will 
apparently bring the two pictures to the same place. 

In Wheatstone's original stereoscope, represented in 
Fig. 35, the observer looked with the right eye into the 
mirror 6, and with the left into the mirror a. Both 
mirrors were placed at an angle to the observer's line of 
sight, and the two pictures were so placed at k and g 
that their reflected images appeared at the same place 
behind the two mirrors ; but the right eye saw the 

1 Described in the Philosophical Transactions for 1838. TB. 


picture g in the mirror 6, while the left saw the picture 
k in the mirror a. 

A more convenient instrument, though it does not 

FIG. 35. 

give sucli sharply defined effects, is the ordinary stereo- 
scope of Brewster, 1 shown in Fig. 36. Here the two 

FIG. 36. 

pictures are placed on the same slide and laid in the 

1 Sir David Brewster, Professor of Mathematics at Edinburgh, boru 
1781, died 1868. TR. 


lower part of the stereoscope, which is divided by a 
partition s. Two slightly prismatic glasses with convex 
surfaces are fixed at the top of the instrument which 
show the pictures somewhat further off, somewhat mag- 
nified, and at the same time overlapping each other, 
so that both appear to be in the middle of the instru- 
ment. The section of the double eye-piece shown in 
Fig. 37 exhibits the position and shape of the right and 
left prisms. Thus both pictures are apparently brought 
to the same spot, and each eye sees only the one which 
belongs to it. 

FIG. 37. 

The illusion prodr.ced by the stereoscope is most 
obvious and striking when other means of recognising 
the form of an object fail. This is the case with geo- 
metrical outlines of solid figures, such as diagrams of 
crystals, and also with representations of irregular objects, 
especially when they are transparent, so that the shadows 
do not fall as we are accustomed to see them in opaque 
objects. Thus glaciers in stereoscopic photographs often 
appear to the unassisted eye an incomprehensible chaos 
of black and white, but when seen through a stereoscope 
the clear transparent ice, with its fissures and polished 
surfaces, comes out as if it were real. It has often 
happened that when I have seen for the first time build- 
ings, cities or landscapes, with which I was familiar 
from stereoscopic pictures, they seemed familiar to 
me ; but I never experienced this impression after see- 
ing any number of ordinary pictures, because these 
but so imperfectly represent the real effect upon the 


The accuracy of the stereoscope is no less wonderful. 
Dove l has contrived an ingenious illustration of this. 
Take two pieces of paper printed with the same type, or 
from the same copper-plate, and hence exactly alike, and 
put them in the stereoscope in place of the two ordinary 
photographs. They will then unite into a single com- 
pletely flat image, because, as we have seen above, the 
two retinal images of a flat picture are identical. But 
no human skill is able to copy the letters of one cop- 
perplate on to another so perfectly that there shall not 
be some difference between them. If, therefore, we print 
off the same sentence from the original plate and a copy 
of it, or the same letters with different specimens of the 
same type, and put the two pieces of paper into the ste- 
reoscope, some lines will appear nearer and some further 
off than the rest. This is the easiest way of detecting 
spurious bank notes. A suspected one is put in a stereo- 
scope along with a genuine specimen of the same kind, 
and it is then at once seen whether all the marks in the 
combined image appear on the same plane. This ex- 
periment is also important for the theory of vision, since 
it teaches us in a most striking manner how vivid, sure, 
and minute is our judgment as to depth derived from 
the combination of the two retinal images. 

We now corne to the question how is it possible for 
two different flat perspective images upon the retina, 
each of them representing only two dimensions, to com- 
bine so as to present a solid image of three dimen- 

1 Heinrich Wilhelm Dove, Professor in the University of Berlin, author 
of Optische Studie.n (1859); also eminent for his researches in meteorology 
and electricity. 

His paper, Anwendung des StereosJcops umfalschcs von cchtcm Papiergdd 
tu unterscheiden, was published in 1859. TB. 


We must first make sure that we are really able to 
distinguish between the two flat images offered us by 
our eyes. If I hold my finger up and look towards the 
opposite wall, it covers a different part of the wall to 
each eye, as I mentioned above. Accordingly I see the 
finger twice, in front of two different places on the wall : 
and if I see a single image of the wall I must see a double 
image of the finger. 

Now in ordinary vision we try to recognise the solid 
form of surrounding objects, and either do not notice this 
double image at all, or only when it is unusually striking. 
In order to see it we must look at the field of vision 
in another way in the way that an artist does who 
intends to draw it. He tries to forget the actual shape, 
size, and distance of the objects that he represents. One 
would think that this is the more simple and original 
way of seeing things ; and hitherto most physiologists 
have regarded it as the kind of vision which results 
most directly from sensation, while they have looked on 
ordinary solid vision as a secondary way of seeing things, 
which has to be learned as the result of experience. But 
every draughtsman knows how much harder it is to 
appreciate the apparent form in which objects appear 
in the field of vision, and to measure the angular 
distance between them, than to recognise what is their 
actual form and comparative size. In fact, the knowledge 
of the true relations of surrounding objects of which the 
artist cannot divest himself, is his greatest difficulty in 
drawing from nature. 

Accordingly, if we look at the field of vision with both 
eyes, in the way an artist does, fixing our attention upon the 
outlines, as they would appear if projected on a pane 
of glass between us and them, we then become at once 
aware of the difference between the two retinal images. 
We see those objects double which lie further off or 


nearer than the point at which we are looking, and are 
not too far removed from it laterally to admit of their 
position being sufficiently seen. At first we can only 
recognise double images of objects at very different 
distances from the eye, but by practice they will be seen 
with objects at nearly the same distance. 

All these phenomena, and others like them, of double 
images of objects seen with both eyes, may be reduced 
to a simple rule which was laid down by Johannes 
Miiller : ' For each point of one retina there is on the 
other a corresponding point/ In the ordinary flat field 
of vision presented by the two e} es, the images received 
by corresponding points as a rule coincide, while images 
received by those which do not correspond do not co- 
incide. The corresponding points in each retina (without 
noticing slight deviations) are those which are situated 
at the same lateral and vertical distance from the point 
of the retina at which rays of light come to a focus when 
we fix the eye for exact vision, namely, the yellow spot. 

The reader will remember that the intuitive theory 
of vision of necessity assumes a complete combination 
of those sensations which are excited by impressions 
upon corresponding ', or, as Miiller calls them, c identical ' 
points. This supposition was most fully expressed in 
the anatomical hypothesis, that two nerve fibres which 
arise from corresponding points of the two retinas actually 
unite so as to form a single fibre, either at the commissure 
of the optic nerves or in the brain itself. I may, how- 
ever, remark that Johannes Miiller did not definitely 
commit himself to this mechanical explanation, although 
he suggested its possibility. He wished his law of iden- 
tical points to be regarded simply as an expression of 
facts, and only insisted that the position in the field of 
vision of the images they receive is always the same. 

But a difficulty arose. The distinction between the 


double images is comparatively imperfect, whenever it is 
possible to combine them into a single view ; a striking 
contrast to the extraordinary precision with which, as 
Dove has shown, we can judge of stereoscopic relief. Yet 
the latter power depends upon the same differences between 
the two retinal pictures which cause the phenomenon of 
double images. The slight difference of distance between 
the objects represented in the right and left half of a 
stereoscopic photograph, which suffices to produce the 
most striking effect of solidity, must be increased twenty 
or thirty-fold before it can be recognised in the produc- 
tion of a double image, even if we suppose the most 
careful observation by one who is well practised in the 

Again, there are a number of other circumstances which 
make the recognition of double images either easy or 
difficult. The most striking instance of the latter is the 
effect of relief. The more vivid the impression of solidity, 
the more difficult are double images to see, so that 
it is easier to see them in stereoscopic pictures than 
in the actual objects they represent. On the other hand, 
the observation of double images is facilitated by varying 
the colour and brightness of the lines in the -two stereo- 
scopic pictures, or by putting lines in both which exactly 
correspond, and so will make more evident by contrast 
the imperfect coalescence of the other lines. All these 
circumstances ought to have no influence, if the com- 
bination of the two images in our sensation depended 
upon any anatomical arrangement of the conducting 

Again, after the invention of the stereoscope, a 
fresh difficulty arose in explaining our perceptions of 
solidity by the differences between the two retinal 
images. First, Briicke * called attention to a series 

1 Professor of Physiology in the University of Vienna. 


of facts which apparently made it possible to reconcile 
the new phenomena discovered with the theory of the 
innate identity of the sensations conveyed by the two 
retingo. If we carefully follow the way in which we 
look at stereoscopic pictures or at real objects, we 
notice that the eye follows the different outlines one 
after another, so that we see the ' fixed point ' at each 
moment single, while the other points appear double. 
But, usually, our attention is concentrated upon the 
fixed point, and we observe the double images so little 
that to many people they are a new and surprising phe- 
nomenon when first pointed out. Now since in following 
the outlines of these pictures, or of an actual image, we 
move the eyes unequally this way and that, sometimes 
they converge, and sometimes diverge, according as we 
look at points of the outline which are apparently nearer 
or further off; and these differences in movement may 
give rise to the impression of different degrees of distance 
of the several lines. 

Now it is quite true, that by this movement of the 
eye while looking at stereoscopic outlines, we gain a 
much more clear and exact image of the raised surface 
they represent, than if we fix our attention upon a single 
point. Perhaps the simple reason is that when we move 
the eyes we look at every point of the figure in suc- 
cession directly ', and therefore see it much more sharply 
defined than when we see only one point directly and the 
others indirectly. But Briicke's hypothesis, that the 
perception of solidity is only produced by this movement 
of the eyes, was disproved by experiments made by Dove, 
which showed that the peculiar illusion of stereoscopic 
pictures is also produced when they are illuminated 
with an electric spark. The light then lasts for less 
than the four thousandth part of a second. In this 
time heavy bodies move so little, even at great velocities, 


that they seem to be at rest. Hence there cannot be the 
slightest movement of the eye, while the spark lasts, 
which can possibly be recognised ; and yet we receive 
the complete impression of stereoscopic relief. 

Secondly, such a combination of the sensations of 
the two eyes as the anatomical hypothesis assumes, is 
proved not to exist by the phenomenon of stereoscopic 
lustre, which was also discovered by Dove. If the same 
surface is made white in one stereoscopic picture and 
black in another, the combined image appears to shine, 
though the paper itself is quite dull. Stereoscopic draw- 
ings of crystals are made so that one shows white lines 
on a black ground, and the other black lines on a white 
ground. When looked at through a stereoscope they give 
the impression of a solid crystal of shining graphite. By 
the same means it is possible to produce in stereoscopic 
photographs the still more beautiful effect of the sheen 
of water or of leaves. 

The explanation of this curious phenomenon is as 
follows : A dull surface, like unglazed white paper, 
reflects the light which falls on it equally in all direc- 
tions, and, therefore, always looks equally bright, from 
whatever point it is seen ; hence, of course, it appears 
equally bright to both eyes. On the other hand, a 
polished surface, beside the reflected light which it 
scatters equally in all directions, throws back other beams 
by regular reflection, which only pass in definite directions. 
Now one eve may receive this regularly reflected light 
and the other not ; the surface will then appear much 
brighter to the one than to the other, and, as this can only 
happen with shining bodies, the effect of the black and 
white stereoscopic pictures appears like that of a polished 

Now if there were a complete combination of the 
impressions produced upon both retinae, the union of 


white and black would give grey. The fact, therefore, 
that when they are actually combined in the stereoscope 
they produce the effect of lustre, that is to say, an 
effect which cannot be produced by any kind of uniform 
grey surface, proves that the impressions on the two 
retinae are not combined into one sensation. 

That, again, this effect of stereoscopic lustre does not 
depend upon an alternation between the perceptions 
of the two eyes, on what is called the ' rivalry of the 
retinae,' is proved by illuminating stereoscopic pictures 
for an instant with the electric spark. The same effect 
is perfectly produced. 

In the third place, it can be proved, not only that the 
images received by the two eyes do not coalesce in our 
sensation, but that the two sensations which we receive 
from the two eyes are not exactly similar, that they can, 
on the contrary, be readily distinguished. For if the sen- 
sation given by the right eye were indistinguishably the 
same as that given by the left, it would follow that, at 
least in the case of the electric spark (when no movements 
of the eye can help us in distinguishing the two images), 
it would make no difference whether we saw the right 
hand stereoscopic picture with the right eye, and the left 
with the left, or put the two pictures into the stereo- 
scope reversed, so as to see that intended for the right 
eye with the left, and that intended for the left eye 
with the right. But practically we find that it makes 
all the difference, for if see make the two pictures change 
places, the relief appears to be inverted : what should be 
further off seems nearer, what should stand out seems 
to fall back. Now, since when we look at objects by 
the momentary light of the electric spark, they always 
appear in their true relief and never reversed, it follows 
that the impression produced on the right eye is not 
indistinguishable from that on the left. 


Lastly, there are some very curious and interesting 
phenomena seen when two pictures are put before the 
two eyes at the same time which cannot be combined so 
as to present the appearance of a single object. If, for 
example, we look with one eye at a page of print, and 
with the other at an engraving, 1 there follows what is 
called the ' rivalry ' of the two fields of vision. The two 
images are not then seen at the same time, one covering 
the other ; but at some points one prevails, and at others 
the other. If they are equally distinct, the places where 
one or the other appears usually change after a few 
seconds. But if the engraving presents anywhere in the 
field of vision a uniform white or black surface, then 
the printed letters which occupy the same position in the 
image presented to the other eye, will usually prevail 
exclusively over the uniform surface of the engraving. In 
spite, however, of what former observers have said to the 
contrary, I maintain that it is possible for the observer at 
any moment to control this rivalry by voluntary direction 
of his attention. If he tries to read the printed sheet, the 
letters remain visible, at least at the spot where for the 
moment he is reading. If, on the contrary, he tries to 
follow the outline and shadows of the engraving, then 
these prevail. I find, moreover, that it is possible to fix 
the attention upon a very feebly illuminated object, and 
make it prevail over a much brighter one, which coincides 
with it in the retinal image of the other eye. Thus, I 
can follow the watermarks of a white piece of paper and 
cease to see strongly-marked black figures in the other 
field. Hence the retinal rivalry is not a trial of strength 
between two sensations, but depends upon, our fixing 

1 The practised observer is able to do this without any apparatus, but 
most persons will find it necessary to put the two objects in a stereoscope 
or, at least, to hold a book, or a sheet of paper, or the hand in front of the 
face, to serve for the partition in the stereoscope. TB. 


on failing to fix the attention. Indeed there is scarcely 
any phenomenon so well fitted for the study of the causes 
which are capable of determining the attention. It is not 
enough to form the conscious intention of seeing first 
with one eye and then with the other ; we must form as 
clear a notion as possible of what we expect to see. Then 
it will actually appear. If, on the other hand, we leave 
the mind at liberty without a fixed intention to ob- 
serve a definite object, that alternation between the two 
pictures ensues which is called retinal rivalry. In this 
case, we find that, as a rule, bright and strongly marked 
objects in one field of vision prevail over those which 
are darker and less distinct in the other, either com- 
pletely or at least for a time. 

We may vary this experiment by using a pair of 
spectacles with different coloured glasses. We shall then 
find, on looking at the same objects with both eyes 
at once, that there ensues a similar rivalry between the 
two colours. Everything appears spotted over first with 
one and then with the other. After a time, however, the 
vividness of both colours becomes weakened, partly by 
the elements of the retina which are affected by each of 
them being tired, and partly by the complementary 
after-images which result. The alternation then ceases, 
and there ensues a kind of mixture of the two original 

It is much more difficult to fix the attention upon a 
colour than upon such an object as an engraving. For the 
attention upon which, as we have seen, the whole phe- 
nomenon of ' rivalry ' depends, fixes itself with constancy 
only upon such a picture as continually offers something 
new for the eye to follow. But we may assist this by 
reflecting on the side of the glasses next the eye letters 
or other lines upon which the attention can fix. These 
reflected images themselves are not coloured, but as soon 


as the attention is fixed upon one of them we become 
conscious of the colour of the corresponding glass. 

These experiments on the rivalry of colours have given 
rise to a singular controversy among the best observers ; 
and the possibility of such difference of opinion is an 
instructive hint as to the nature of the phenomenon 
itself. One party, including the names of Dove, Reg- 
nault, 1 Briicke, Ludwig, 2 Panum, 3 and Hering, 4 main- 
tains that the result of a binocular view of two colours 
is the true combination-colour. Other observers, as 
Heinrich Meyer of Zurich, Volkmann, Meissner, 5 and 
Funke, 6 declare quite as positively that, under these 
conditions, they have never seen the combination-colour. 
I myself entirely agree with the latter, and a careful 
examination of the cases in which I might have imagined 
that I saw the combination-colour, has always proved to 
me that it was the result of phenomena of contrast. 
Each time that I brought the true combination-colour 
side by side with the binocular mixture of colours, the 
difference between the two was very apparent. On the 
other hand, there can of course be no doubt that the ob- 
servers I first named really saw what they profess, so that 
there mast here be great individual difference. Indeed 
with certain experiments which Dove recommends as par- 
ticularly well fitted to prove the correctness of his con- 
clusion, such as the binocular combination of comple- 
mentary polarisation-colours into white, I could not 
myself see the slightest trace of a combination-colour. 

1 The distinguished French chemist, father of the well-known painter 
who was killed in the second siege of Paris. 

2 Professor of Physiology in the University of Leipzig. 

3 Professor of Physiology in the University of Kiel. 

4 Ewald Hering, Professor of Physiology in the University of Prague, 
lately in the Josephsakademie of Vienna. 

5 Professor of Physiology in the University of Gottingen. 

6 Professor of Physiology in the University of Freiburg. Ta. 


This striking* difference in a comparatively simple 
observation seems to me to be of great interest. It is a 
remarkable confirmation of the supposition above made, 
in accordance with the empirical theory of vision, that in 
general only those sensations are perceived as separated 
in space, which can be separated one from another by 
voluntary movements. Even when we look at a compound 
colour with one eye, only three separate sensations are, ac- 
cording to Young's theory, produced together ; but it is 
impossible to separate these by any movement of the 
eye, so that they always remain locally united. Yet we 
have seen that even in this case we may become conscious 
of a separation under certain circumstances; namely, 
when it is seen that part of the colour belongs to a 
transparent covering. When two corresponding points 
of the retinae are illuminated with different colours, it 
will be rare for any separation between them to appear in 
ordinary vision ; if it does, it will usually take place in 
the part of the field of sight outside the region of exact 
vision. But there is always a possibility of separating 
the compound impression thus produced into its two 
parts, which will appear to some extent independent of 
each other, and will move with the movements of the 
eye; and it will depend upon the degree of attention 
which the observer is accustomed to give to the region 
of indirect vision and to double images, whether he 
is able to separate the colours which fall on both retinae 
at the same time. Mixed hues, whether looked at with 
one eye or with both, excite many simple sensations 
of colour at the same time, each having exactly the 
same position in the field of vision. The difference in 
the way in which such a compound-colour is regarded 
by different people depends upon whether this compound 
sensation is at once accepted as a coherent whole without 
any attempt at analysis, or whether the observer is able 


by practice to recognise the parts of which it is com- 
posed, and to separate them from one another. The 
former is our usual (though not constant) habit when 
looking with one eye, while we are more inclined to the 
latter when using both. But inasmuch as this incli- 
nation must chiefly depend upon practice in observing 
distinctions, gained by preceding observation, it is easy 
to understand how great individual peculiarities may 

If we carefully observe the rivalry which ensues when 
we try to combine two stereoscopic drawings, one of which 
is in black lines on a white ground and the other in 
white lines on black, we shall see that the white and 
black lines which affect nearly corresponding points of each 
retina always remain visible side by side an effect which 
of course implies that the white and black grounds are 
also visible. By this means the brilliant surface, which 
seems to shine like black lead, makes a much more stable 
impression than that produced under the operation of 
retinal rivalry by entirely different drawings. If we 
cover the lower half of the white figure on a black ground 
with a sheet of printed paper, the upper half of the com- 
bined stereoscopic image shows the phenomenon of Lustre, 
while in the lower we see Retinal Rivalry between the 
black lines of the figure and the black marks of the 
type. As long as the observer attends to the solid form 
of the object represented, the black and white outlines 
of the two stereoscopic drawings carry on in common the 
point of exact vision as it moves along them, and the 
effect can only be kept up by continuing to follow both. 
He must steadily keep his attention upon both drawings, 
and then the impression of each will be equally combined. 
There is no better way of preserving the combined effect 
of two stereoscopic pictures than this. Indeed it is 
possible to combine (at least partially and for a short 


time) two entirely different drawings when put into the 
stereoscope, by fixing the attention upon the way in 
which they cover each other, watching, for instance, the 
angles at which their lines cross. But as soon as the 
attention turns from the angle to follow one of the lines 
which makes it, the picture to which the other line 
belongs vanishes 

Let us now put together the results to which our 
inquiry into binocular vision has led us. 

I. The excitement of corresponding points of the two 
retinae is not indistinguishably combined into a single 
impression ; for, if it were, it would be impossible to see 
Stereoscopic Lustre. And we have found reason to believe 
that this effect is not a consequence of Ketinal Eivalry, 
even if we admit the latter phenomenon to belong to 
sensation at all, and not rather to the degree of attention. 
On the contrary the appearance of lustre is associated 
with the restriction of this rivalry. 

II. The sensations which are produced by the excita- 
tion of corresponding points of each retina are not in- 
distinguishably the same ; for otherwise we should not 
be able to distinguish the true from the inverted or 
6 pseudoscopic ' relief, when two stereoscopic pictures are 
illuminated by the electric spark. 

III. The combination of the two different sensations 
received from corresponding retinal points is not pro- 
duced by one of them being suppressed for a time ; 
for, in the first place, the perception of solidity given by 
the two eyes depends upon our being at the same time 
conscious of the two different images, and, in the second, 
this perception of solidity is independent of any move- 
ment of the retinal images, since it is possible under 
momentary illumination. 

We therefore learn that two distinct sensations are trans- 


mitted from the two eyes, and reach the consciousness 
at the same time and without coalescing ; that accordingly 
the combination of these two sensations into the single 
picture of the external world of which we are conscious 
in ordinary vision is not produced by any anatomical 
mechanism of sensation, but by a mental act. 

IV. Further, we find that there is, on the whole, com- 
plete, or at least nearly complete, coincidence as to 
localisation in the field of vision of impressions of sight 
received from corresponding points of the retinae ; but 
that when we refer both impressions to the same object, 
their coincidence of localisation is much disturbed. 

If this coincidence were the result of a direct function 
of sensation, it could not be disturbed by the mental 
operation which refers the two impressions to the same 
object. But we avoid the difficulty, if we suppose that 
the coincidence in localisation of the corresponding 
pictures received from the two eyes depends upon the 
power of measuring distances at sight which we gain by 
experience, that is, on an acquired knowledge of the 
meaning of the signs of localisation.' In this case it is 
simply one kind of experience opposing another ; and 
we can then understand how the conclusion that two 
images belong to the same object should influence our 
estimation of their relative position by the measuring 
power of the eye, and how in consequence the distance 
Df the two images from the fixed point in the field of 
vision should be regarded as the same, although it is not 
exactly so in reality. 

But if the practical coincidence of corresponding points 
as to localisation in the two fields of vision does not 
depend upon sensation, it follows that the original power 
of comparing different distances in each separate field of 
vision cannot depend upon direct sensation. For, if it 
were so, it would follow that the coincidence of the two 


fields would be completely established by direct sensation, 
as soon as the observer had got his two fixed points to 
coincide and a single meridian of one eye to coincide 
with the corresponding one of the other. 

The reader sees how this series of facts has driven us 
by force to the empirical theory of vision. It is right to 
mention that lately fresh attempts have been made to 
explain the origin of our perception of solidity and the 
phenomena of single and double binocular vision by the 
assumption of some ready-made anatomical mechanism. 
We cannot criticise these attempts here : it would lead 
us too far into details. Although many of these hypo- 
theses are very ingenious (and at the same time very 
indefinite and elastic), they have hitherto always proved 
insufficient ; because the actual world offers us far more 
numerous relations than the authors of these attempts 
could provide for. Hence, as soon as they have arranged 
one of their systems to explain any particular phe- 
nomenon of vision, it is found not to answer for any 
other. Then, in order to help out the hypothesis, 
the very doubtful assumption has to be made that, in 
these other cases, sensation is overcome and extinguished 
by opposing experience. But what confidence could we 
put in any of our perceptions if we were able to extinguish 
our sensations as we please, whenever they concern an 
object of our attention, for the sake of previous concep- 
tions to which they are opposed ? At any rate, it is clear 
that in every case where experience must finally decide, 
we shall succeed much better in forming a correct notion 
of what we see, if we have no opposing sensations to 
overcome, than if a correct judgment must -be formed in 
spite of them. 

It fo^pws that the hypotheses which have been suc- 
jh^ely framed by the various supporters of intuitive 


theories of vision, in order to suit one phenomenon after 
another, are really quite unnecessary. No fact has 
yet been discovered inconsistent with the Empirical 
Theory : which does not assume any peculiar modes , 
of physiological action in the nervous system, nor any 
hypothetical anatomical structures; which supposes no- 
thing more than the well known association between the 
impressions we receive and the conclusions we draw from 
them, according to the fundamental laws of daily ex- 
perience. It is true that we cannot at present offer any 
complete scientific explanation of the mental operations 
involved, and there is no immediate prospect of our doing 
so. But since these operations actually exist, and since 
hitherto every form of the intuitive theory has been 
obliged to fall back on their reality when all other 
explanation failed, these mysteries of the laws of thought 
cannot be regarded from a scientific point of view as con- 
stituting any deficiency in the empirical theory of vision. 

It is impossible to draw any line in the study of our 
perceptions of space which shall sharply separate those 
which belong to direct Sensation from those \vhich are 
the result of Experience. If we attempt to draw such 
a boundary, we find that experience proves more minute, 
more direct and more exact than supposed sensation, 
and in fact proves its own superiority by overcoming the 
latter. The only supposition which does not lead to any 
contradiction is that of the Empirical Theory, which 
regards all our perceptions of space as depending upon 
experience, and not only the qualities, but even the 
local signs of the sense of sight as nothing more than 
signs, the meaning of which we have to learn by ex- 

We become acquainted with their meaning by com- 
paring them with the result of our own movements, with 


the changes which we thus produce in the outer world. 
The infant first begins to play with its hands. There is 
a time when it does not know how to turn its eyes or 
its hands to an object which attracts its attention by its 
brightness or colour. When a little older, a child seizes 
whatever is presented to it, turns it over and over again, 
looks at it, touches it, and puts it in his mouth. The 
simplest objects are what a child likes best, and he 
always prefers the most primitive toy to the elaborate 
inventions of modern ingenuity. After he has looked at 
such a toy every day for weeks together, he learns at last 
all the perspective images which it presents; then he 
throws it away and wants a fresh toy to handle like the 
first. By this means the child learns to recognise the 
different views which the same object can afford, in 
connection with the movements which he is constantly 
giving it. The conception of the shape of any object, 
gained in this manner, is the result of associating all 
these visual images. When we have obtained an accurate 
conception of the form of any object, we are then able 
to imagine what appearance it would present, if we looked 
at it from some other point of view. All these different 
views are combined in the judgment we form as to the 
dimensions and shape of an object. And, consequently, 
when we are once acquainted with this, we can deduce 
from it the various images it would present to the sight 
when seen from different points of view, and the various 
movements which we should have to impress upon it in 
order to obtain these successive images. 

I have often noticed a striking instance of what I have 
been saying in looking at stereoscopic pictures. If, for 
example, we look at elaborate outlines of complicated 
crystalline forms, it is often at first difficult to see what 
they mean. When this is the case, I look out two points 


in the diagram which correspond, and make them overlap 
by a voluntary movement of the eyes. But as long as I 
.have not made out what kind of form the drawings are in- 
tended to represent, I find that my eyes begin to diverge 
again, and the two points no longer coincide. Then I try 
to follow the different lines of the figure, and suddenly I 
see what the form represented is. From that moment my 
two eyes pass over the outlines of the apparently solid 
body with the utmost ease, and without ever separating. 
As soon as we have gained a correct notion of the shape 
of an object, we have the rule for the movements of the 
eyes which are necessary for seeing it. In carrying out 
these movements, and thus receiving the visual impres- 
sions we expect, we retranslate the notion we have formed 
into reality, and by finding this retranslation agrees with 
the original, we become convinced of the accuracy of our 

This last point is, I believe, of great importance. 
The meaning we assign to our sensations depends upon 
experiment, and not upon mere observation of what takes 
place around us. We learn by experiment that the cor- 
respondence between two processes takes place at any 
moment that we choose, and under conditions which we 
can alter as we choose. Mere observation would not giv.e 
us the same certainty, even though often repeated under 
different conditions. For we should thus only learn that 
the processes in question appear together frequently (or 
even always, as far as our experience goes) ; but mere 
observation would not teach us that they appear together 
at any moment we select. 

Even in considering examples of scientific observation, 
methodically carried out, as in astronomy, meteorology, 
or geology, we never feel fully convinced of the causes of 
the phenomena observed until we can demonstrate the 
working of these same forces by actual experiment in 


the laboratory. So long as science is not experimental 
it does not teach us the knowledge of any new force. 1 

It is plain that, by the experience which we collect in 
the way I have been describing, we are able to learn . 
as much of the meaning of sensible ' signs ' as can 
afterwards be verified by further experience; that is to 
say, all that is real and positive in our conceptions. 

It has been hitherto supposed that the sense of touch 
confers the notion of space and movement. At first 
of course the only direct knowledge we acquire is that 
we can produce, by an act of volition, changes of 
which we are cognisant by means of touch and sight. 
Most of these voluntary changes are movements, or 
changes in the relations of space ; but we can also pro- 
duce changes in an object itself. Now, can we recognise 
the movements of our hands and eyes as changes in the 
relations of space, without knowing it beforehand ? and 
can we distinguish them from other changes which affect 
the properties of external objects ? I believe we can. It 
is an essentially distinct character of the Relations of 
Space that they are changeable relations betiveen objects 
which do not depend on their quality or quantity, while all 
other material relations between objects depend upon their 
properties. The perceptions of sight prove this directly 
and easily. A movement of the eye which causes the 
retiral image to shift its place upon the retina always 
produces the same series of changes as often as it is 
repeated, whatever objects the field of vision may con- 
tain. The effect is that the impressions which had 
before the local signs , a 1? a 2 , a& receive the new local 
signs b oy 6 1? 6 2 , 6 3 ; and this may always occur in the same 

1 An interesting paper, applying this view of the 'experimental' cha- 
racter of progressive science to Zoology, has been published by M. Lacaze 
Duthiers, in the first number of his Archives de Zoologie. TR. 


way, whatever be the quality of the impressions. By 
this means we learn to recognise such changes as be- 
longing to the special phenomena which we call changes 
in space. This is enough for the object of Empirical 
Philosophy, and we need not further enter upon a dis- 
cussion of the question, how much of universal concep- 
tions of space is derived a priori, and how much a 
posteriori ? l 

An objection to the empirical Theory of Vision might 
be found in the fact that illusions of the senses are 
possible ; for if we have learnt the meaning of our 
sensations from experience, they ought always to agree 
with experience. The explanation of the possibility of 
illusions lies in the fact that we transfer the notions 
of external objects, which would be correct under normal 
conditions, to cases in which unusual circumstances have 
altered the retinal pictures. What I call ' observation 
under normal conditions ' implies not only that the rays of 
light must pass in straight lines from each visible point 
to the cornea, but also that we must use our eyes in the 
way they should be used in order to receive the clearest 
and most easily distinguishable images. This implies 
that we should successively bring the images of the 
separate points of the outline of the objects we are 
looking at upon the centres of both retinae (the yellow 
spot), and also move the eyes so as to obtain the surest 
comparison between their various positions. When- 
ever we deviate from these conditions of normal vision, 
illusions are the result. Such are the long recognised 
effects of the refraction or reflection of rays of light 
before they enter the eye. But there are many other 

1 The question of the origin of our conceptions of space is discussed by 
Mr. Bain on empirical principles in his treatise on The Senses and the In- 
tellect, pp. 114-118, 189-194, 245, 363-392, &c. TR. 


causes of mistake as to the position of the objects we 
see defective accommodation when looking through one 
or two small openings, improper convergence when 
looking with one eye only, irregular position of the 
eye-ball from external pressure or from paralysis of its 
muscles. Moreover, illusions may come in from certain 
elements of sensation not being accurately distinguished ; 
as, for instance, the degree of convergence of the two 
eyes, of which it is difficult to form an accurate judgment 
when the muscles which produce it become fatigued. 

The simple rule for all illusions of sight is this : we 
always believe that we see such objects as would, under 
conditions of normal vision, produce the retinal image 
of which we are actually conscious. If these images are 
such as could not be produced by any normal kind of 
observation, we judge of them according to their nearest 
resemblance; and in forming this judgment, we more 
easily neglect the parts of sensation which are imperfectly 
than those which are perfectly apprehended. When more 
than one interpretation is possible, we usually waver 
involuntarily between them ; but it is possible to end 
this uncertainty by bringing the idea of any of the 
possible interpretations we choose as vividly as possible 
before the mind by a conscious effort of the will. 

These illusions obviously depend upon mental processes 
which may be described as false inductions. But there 
are, no doubt, judgments which do not depend upon 
our consciously thinking over former observations of the 
same kind, and examining whether they justify the 
conclusion which we form. I have, therefore, named 
these 'unconscious judgments;' and this term, though 
accepted by other supporters of the empirical theory, 
has excited much opposition, because, according to 
generally-accepted psychological doctrines, & judgment, 


or logical conclusion, is the culminating point of the 
conscious operations of the mind. But the judgments 
which play so great a part in the perceptions we derive 
from our senses cannot be expressed in the ordinary 
form of logically analysed conclusions, and it is neces- 
sary to deviate somewhat from the beaten paths of psy- 
chological analysis in order to convince ourselves that 
we really have here the same kind of mental operation 
as that involved in conclusions usually recognised as 
such. There appears to me to be in reality only a super- 
ficial difference between the 'conclusions' of logicians 
and those inductive conclusions of which we recognise the 
result in the conceptions we gain of the outer world 
through our sensations. The difference chiefly depends 
upon the former conclusions being capable of expression 
in words, while the latter are not ; because, instead of 
words, they only deal with sensations and the memory 
of sensations. Indeed, it is just the impossibility of 
describing sensations, whether actual or remembered, in 
words, which makes it so difficult to discuss this depart- 
ment of psychology at all. 

Beside the knowledge which has to do with Notions, 
and is, therefore, capable of expression in words, there is 
another department of our mental operations, which may 
be described as knowledge of the relations of thoso 
impressions on the senses which are not capable of direct 
verbal expression. For instance, when we say that we 
' know ' 1 a man, a road, a fruit, a perfume, we mean that 
we have seen, or tasted, or smelt, these objects. We 
keep the sensible impression fast in our memory, and we 
shall recognise it again when it is repeated, but we 

1 In German this kind of knowledge is expressed by the verb Jcennen 
(cognoscere, connaitre), to be acquainted with, while wissen (scire, savoir) 
means to be aware of. The former kind of knowledge is only applicable to 
objects directly cognisable by the senses, whereas the latter applies to 
notions or conceptions which can be ^ormally stated as propositions. TR. 


cannot describe the impression in words, even to our- 
selves. And yet it is certain that this kind of know- 
ledge (Kenneru) may attain the highest possible degree 
of precision and certainty, and is so far not inferior 
to any knowledge (Wisseri) which can be expressed in 
words ; but it is not directly communicable, unless the 
object in question can be brought actually forward, or 
the impression it produces can be otherwise represented 
as by drawing the portrait of a man instead of pro- 
ducing the man himself. 

It is an important part of the former kind of know- 
ledge to be acquainted with the particular innervation of 
muscles, which is necessary in order to produce any effect 
we intend by moving our limbs. As children, we must 
learn to walk ; we must afterwards learn how to skate or 
go on stilts, how to ride, or swim, or sing, or pronounce a 
foreign language. Moreover, observation of infants shows 
that they have to learn a number of things which after- 
wards they will know so well as entirely to forget that 
there was ever a time when they were ignorant of them. 
For example, everyone of us had to learn, when an 
infant, how to turn his eyes toward the light in order to 
see. This kind of ' knowledge ' (Kennen) we also call 
6 being able ' to do a thing (konnen), or 6 understanding ' 
how to do it (versteheri), as, ' I know how to ride,' ' I am 
able to ride,' or ' I understand how to ride.' l 

It is important to notice that this ; knowledge ' of the 
effort of the will to be exerted must attain the highest 
possible degree of certainty, accuracy, and precision, for 
us to be able to maintain so artificial a balance as is 
necessary for walking on stilts or for skating, for the singer 
to know how to strike a note with his voice, or the 

1 The German word Jconnen is said to be of the same etymology as 
Iccnncn, and so their likeness in form would be explained by their likeness 
in meaning. 


violin-player with his finger, so exactly that its vibration 
shall not be out by a hundredth part. 

Moreover, it is clearly possible, by using these sensible 
images of memory instead of words, to produce the same 
kind of combination which, when expressed in words, 
would be called a proposition or a conclusion. For 
example, I may know that a certain person with whose 
face I am familiar, has a peculiar voice, of which I have 
an equally lively recollection. I should be able with 
the utmost certainty to recognise his face and his voice 
among a thousand, and each would recall the other. But 
I cannot express this fact in words, unless I am able to 
add some other characters of the person in question 
which can be better denned. Then I should be able to 
resort to a syllogism and say, ' This voice which I now 
hear belongs to the man whom I saw then and there.' 
But universal, as well as particular conclusions, may be 
expressed in terms of sensible impressions, instead of 
words. To prove this I need only refer to the effect of 
works of art. The statue of a god would not be 
capable of conveying a notion of a definite character and 
disposition, if I did not know that the form of face and 
the expression it wears have usually or constantly a cer- 
tain definite signification. And, to keep in the domain 
of the perceptions of the senses, if I know that a par- 
ticular way of looking, for which I have learnt how to 
employ exactly the right kind of innervation, is necessary 
in order to bring into direct vision a point two feet off 
and so many feet to the right, this also is a universal 
proposition which applies to every case in which I have 
fixed a given point at that distance before, or may do so 
hereafter. It is a piece of knowledge which cannot be 
expressed in words, but is the result which sums up my 
previous successful experience. It may at any moment 
become the major premiss of a syllogism, whenever, in 
fact, I fix a point in the supposed position and feel that I 


do so by looking as that major proposition states. This 
perception of what I am doing is my minor proposition, 
and the 6 conclusion' is that the object I am looking for 
will be found at the spot in question. 

Suppose that I employ the same way of looking, but look 
into a stereoscope. I am now aware that there is no real 
object before me at the spot I am looking at ; but I have the 
same sensible impression as if one were there ; and yet I 
am unable to describe this impression to myself or others, 
or to characterise it otherwise than as ' the same impression 
which would arise in the normal method of observation, if 
an object were really there.' It is important to notice this. 
No doubt the physiologist can describe the impression 
in other ways, by the direction of the eyes, the position 
of the retinal images, and so on ; but there is no other 
way of directly denning and characterising the sensation 
which we experience. Thus we may recognise it as an 
illusion, but yet we cannot get rid of the sensation of this 
illusion ; for we cannot extinguish our remembrance of 
its normal signification, even when we know that in the 
case before us this does not apply just as little as we 
are able to drive out of the mind the meaning of a 
word in our mother tongue, when it is employed as a 
sign for an entirely different purpose. 

These conclusions in the domain of our sensible per- 
ceptions appear as inevitable as one of the forces of 
nature, and hence their results seem to be directly ap- 
prehended, without any effort on our part ; but this 
does not distinguish them from logical and conscious 
conclusions, or at least from those which really deserve 
the name. All that we can do by voluntary and con- 
scious effort, in order to come to a conclusion, is, after 
all, only to supply complete materials for constructing the 
necessary premisses. As soon as this is done, the conclu- 
sion forces itself upon us. Those conclusions which (it is 


supposed) may be accepted or avoided as we please, are 
not worth much. 

The reader will see that these investigations have led 
us to a field of mental operations which has been seldom 
entered by scientific explorers. The reason is that it is 
difficult to express these operations in words. They have 
been hitherto most discussed in writings on aesthetics, 
where they play an important part as Intuition, Uncon- 
scious Eatioci nation, Sensible Intelligibility, and such 
obscure designations. There lies under all these phrases 
the false assumption that the mental operations we are 
discussing take place in an undefined, obscure, half- 
conscious fashion ; that they are, so to speak, mechanical 
operations, and thus subordinate to conscious thought, 
which can be expressed in language. I do not believe 
that any difference in kind between the two functions 
can be proved. The enormous superiority of knowledge 
which has become ripe for expression in language, is 
sufficiently explained by the fact that, in the first place, 
speech makes it possible to collect together the ex- 
perience of millions of individuals and thousands of 
generations, to preserve them safely, and by continual 
verification to make them gradually more and more 
certain and universal; while, in the second place, all 
deliberately combined actions of mankind, and so the 
greatest part of human power, depend on language. In 
neither of these respects can mere familiarity with phe- 
nomena (das Kenneri) compete with the knowledge of 
them which can be communicated by speech (das Wis- 
seri) ; and yet it does not follow of necessity that the 
one kind of knowledge should be of a different nature 
from the other, or less clear in its operation. 

The supporters of Intuitive Theories of Sensation often 
appeal to the capabilities of new-born animals, many of 


which show themselves much more skilful than a human 
infant. It is quite clear that an infant, in spite of the 
greater size of its brain, and its power of mental develop- 
ment, learns with extreme slowness to perform the 
simplest tasks ; as, for example, to direct its eyes to an 
object cr to touch what it sees with its hands. Must we 
not conclude that a child has much more to learn than 
an animal which is safely guided, but also restricted, 
by its instincts ? It is said that the calf sees the udder 
and goes after it, but it admits of question whether it 
does not simply smell it, and make those movements 
which bring it nearer to the scent. 1 At any rate, the 
child knows nothing of the meaning of the visual image 
presented by its mother's breast. It often turns obsti- 
nately away from it to the wrong side and tries to find 
it there. The young chicken very soon pecks at grains 
of corn, but it pecked while it was still in the shell, 
and when it hears the hen peck, it pecks again, at first 
seemingly at random. Then, when it has by chance hit 
upon a grain, it may, no doubt, learn to notice the field 
of vision which is at the moment presented to it. The 
process is all the quicker because the whole of the mental 
furniture which it requires for its life is but small. 

We need, however, further investigations on the sub- 
ject in order to throw light upon this question. As far 
as the observations with which I am acquainted go, they 
do not seem to me to prove that anything more than 
certain tendencies is born with animals. At all events 
one distinction between them and man lies precisely in 
this, that these innate or congenital tendencies, im- 
pulses or instincts are in him reduced to the smallest 
possible number and strength. 2 

1 See Darwin on the Expression of the Emotions, p. 47. TR. 
* See on this subject Bain on the Senses and tJie Intellect, p. 293 ; also a 
paper on 'Instinct' in Nature, Oct. 10, 1872. 



There is a most striking analogy between the entire 
range of processes which we have been discussing, and 
another System of Signs, which is not given by nature 
but arbitrarily chosen, and which must undoubtedly be 
learned before it is understood. I mean the words of our 
mother tongue. 

Learning how to speak is obviously a much more 
difficult task than acquiring a foreign language in after 
life. First, the child has to guess that the sounds it 
hears are intended to be signs at all ; next, the meaning 
of each separate sound must be found out, by the same 
kind of induction as the meaning of the sensations of 
sight or touch; and yet we see children by the end 
of their first year already understanding certain words 
and phrases, even if they are not yet able to repeat 
them. We may sometimes observe the same in dogs. 

Now this connection between Names and Objects, which 
demonstrably must be learnt, becomes just as firm and 
indestructible as that between Sensations and the Objects 
which produce them. We cannot help thinking of the 
usual signification of a word, even when it is used 
exceptionably in some other sense ; we cannot help feeling 
the mental emotions which a fictitious narrative calls 
forth, even when we know that it is not true ; just in the 
same way as we cannot get rid of the normal signification 
of the sensations produced by any illusion of the senses, 
even when we know that they are not real. 

There is one other point of comparison which is worth 
notice. The elementary signs of language are only twenty- 
six letters, and yet what wonderfully varied meanings 
;an we express and communicate by their combination ! 
Consider, in comparison with this, the enormous number 
of elementary signs with which the machinery of sight 
is provided. We may take the number of fibres in the 
optic nerves as two hundred and fifty thousand. Each 


of these is capable of innumerable different degrees of 
sensation of one, two, or three primary colours. It 
follows that it is possible to construct an immeasurably 
greater number of combinations here than with the few 
letters which build up our words. Nor must we forget 
the extremely rapid changes of which the images of sight 
are capable. No wonder, then, if our senses speak to us 
in language which can express far more delicate distinc- 
tions and richer varieties than can be conveyed by words. 

This is the solution of the riddle of how it is possible 
to see; and, as far as I can judge, it is the only one 
of which the facts at present known admit. Those 
striking and broad incongruities between Sensations and 
Objects, both as to quality and to localisation, on which 
we dwelt, are just the phenomena which are most in- 
structive ; because they compel us to take the right road. 
And even those physiologists who try to save fragments 
of a pre-established harmony between sensations and 
their objects, cannot but confess that the completion and 
refinement of sensory perceptions depend so largely upon 
experience, that it must be the latter which finally 
decides whenever they contradict the supposed congenital 
arrangements of the organ. Hence the utmost signi- 
ficance which may still be conceded to any such anatomi- 
cal arrangements is that they are possibly capable of 
helping the first practice of our senses. 

The correspondence, therefore, between the external 
world and the Perceptions of Sight rests, either in whole 
or in part, upon the same foundation as all our know- 
ledge of the actual world on experience, and on constant 
Verification of its accuracy by experiments which we 
perform with every movement of our body. It follows, 
of course, that we are only warranted in accepting the 
reality of this correspondence so far as these means of 


verification extend, which is really as far as for practical 
purposes we need. 

Beyond these limits, as, for example, in the region of 
Qualities, we are in some instances able to prove con- 
clusively that there is no correspondence at all between 
sensations and their objects. 

Only the relations of time, of space, of equality, and 
those which are derived from them, of number, size, 
regularity of coexistence and of sequence c mathematical 
relations' in short are common to the outer and the 
inner world, and here we may indeed look for a complete 
correspondence between our conceptions and the objects 
which excite them. 

But it seems to me that we should not quarrel with 
the bounty of nature because the greatness, and also the 
emptiness, of these abstract relations have been concealed 
from us by the manifold brilliance of a system of signs ; 
since thus they can be the more easily surveyed and used 
for practical ends, while yet traces enough remain visible 
to guide the philosophical spirit aright, in its search after 
the meaning of sensible Images and Signs. 



As I have undertaken to deliver here a series of lectures, 
I think the best way in which I can discharge that duty 
will be to bring before you, by means of a suitable 
example, some view of the special character of those 
sciences to the study of which I have devoted myself. 
The natural sciences, partly in consequence of their 
practical applications, and partly from their intellectual 
influence on the last four centuries, have so profoundly, 
and with such increasing rapidity, transformed all the 
relations of the life of civilised nations; they have 
given these nations such increase of riches, of enjoy- 
ment of life, of the preservation of health, of means of 
industrial and of social intercourse, and even such in- 
crease of political power, that every educated man who 
tries to understand the forces at work in the world in 
which he is living, even if he does not wish to enter upon 
the study of a special science, must have some interest 
in that peculiar kind of mental labour which works and 
acts in the sciences in question. 

On a former occasion I have already discussed the 
characteristic differences which exist between the natural 
and the mental sciences as regards the kind of scientific 
work. I then endeavoured to show that it is more 


especially in the thorough conformity with law which 
natural phenomena and natural products exhibit, and 
in the comparative ease with which laws can be stated, 
that this difference exists. Not that I wish by any means 
to deny, that the mental life of individuals and peoples 
is also in conformity with law, as is the object of philo- 
sophical, philological, historical, moral, and social sciences 
to establish. But in mental life, the influences are so 
interwoven, that any definite sequence can but seldom 
be demonstrated. In Nature the converse is the case. 
It has been possible to discover the law of the origin 
and progress of many enormously extended series of 
natural phenomena with such accuracy and completeness 
that we can predict their future occurrence with the 
greatest certainty; or in cases in which we have power 
over the conditions under which they occur, we can 
direct them just according to our will. The greatest 
of all instances of what the human mind can effect by 
means of a well-recognised law of natural phenomena 
is that afforded by modern astronomy. The one simple 
law of gravitation regulates the motions of the heavenly 
bodies not only of our own planetary system, but also of 
the far more distant double stars ; from which, even the 
ray of light, the quickest of all messengers, needs years 
to reach our eye; and just on account of this simple 
conformity with law, the motions of the bodies in ques- 
tion, can be accurately predicted and determined both 
for the past and for future years and centuries to a frac- 
tion of a minute. 

On this exact conformity with law depends also the 
certainty with which we know how to tame the impetuous 
force of steam, and to make it the obedient servant of our 
wants. On this conformity depends, moreover, the intel- 
lectual fascination which chains the physicist to his sub- 
jects. It is an interest of quite a different kind to that 


which mental and moral sciences afford. In the latter it 
is man in the various phases of his intellectual activity 
who chains us. Every great deed of which history tells 
us, every mighty passion which art can represent, every 
picture of manners, of civic arrangements, of the culture 
of peoples of distant lands, or of remote times, seizes and 
interests us, even if there is no exact scientific connec- 
tion among them. We continually find points of contact 
and comparison in our own conceptions and feelings ; 
we get to know the hidden capacities and desires of the 
mind, which in the ordinary peaceful course of civilised 
life remain unawakened. 

It is not to be denied that, in the natural sciences, this 
kind of interest is wanting. Each individual fact, taken 
of itself, can indeed arouse our curiosity or our astonish- 
ment, or be useful to us in its practical applications. But 
intellectual satisfaction we obtain only from a connection 
of the whole, just from its conformity with law. Reason 
we call that faculty innate in us of discovering laws and 
applying them with thought. For the unfolding of the 
peculiar forces of pure reason in their entire certainty and 
in their entire bearing, there is no more suitable arena than 
inquiry into nature in the wider sense, the mathematics 
included. And it is not only the pleasure at the success- 
ful activity of one of our most essential mental powers ; 
and the victorious subjections to the power of our thought 
and will of an external world, partly unfamiliar, and partly 
hostile, which is the reward of this labour ; but there is a 
kind, I might almost say, of artistic satisfaction, when we 
are able to survey the enormous wealth of Nature as a 
regularly-ordered whole a kosmos, an image of the 
logical thought of our own mind. 

The last decades of scientific development have led us 
to the recognition of a new universal law of all natural 
phenomena, which, from its extraordinarily extended range. 


and from the ~ connection which it constitutes between 
natural phenomena of all kinds, even of the remotest 
times and the most distant places, is especially fitted to 
give us an idea of what I have described as the character 
of the natural sciences, which I have chosen as the sub- 
ject of this lecture. 

This law is the Law of the Conservation of Force, a 
term the meaning of which I mast first explain. It is not 
absolutely new ; for individual domains of natural pheno- 
mena it was enunciated by Newton and Daniel Ber- 
noulli ; and Rumford and Humphry Davy have recognised 
distinct features of its presence in the laws of heat. 

The possibility that it was of universal application was 
first stated by Dr. Julius Robert Mayer, a Schwabian 
physician (now living in Heilbronn) in the year 1842, 
while almost simultaneously with, and independently of 
him, James Prescot Joule, an English manufacturer, made 
a series of important and difficult experiments on the rela- 
tion of heat to mechanical force, which supplied the chief 
points in which the comparison of the new theory with 
experience was still wanting. 

The law in question asserts, that the quantity of force 
which can be brought into action in the whole of Nature 
is unchangeable, and can neither be increased nor di- 
minished. My first object will be to explain to you what 
is understood by quantity of force ; or as the same idea 
is more popularly expressed with reference to its technical 
application, what we call amount of work in the me- 
chanical sense of the word. 

The idea of work for machines, or natural processes, is 
taken from comparison with the working power of man ; 
and we can therefore best illustrate from human labour, 
the most important features of the question with which 
we are concerned. In speaking of the work of machines, 
and of natural forces, we must, of course, in this compari- 


son eliminate anything in which activity of intelligence 
comes into play. The latter is also capable of the hard 
and intense -work of thinking, which tries a man just as 
muscular exertion does. But whatever of the actions of 
intelligence is met with in the work of machines, of course 
is due to the mind of the constructor and cannot be 
assigned to the instrument at work. 

Now, the external work of man is of the most varied 
kind as regards the force or ease, the form and rapidity, 
of the motions used on it, and the kind of work produced. 
But both the arm of the blacksmith who delivers his 
powerful blows with the heavy hammer, and that of the 
violinist who produces the most delicate variations in 
sound, and the hand of the lace-maker who works with 
threads so fine that they are on the verge of the invisible, 
all these acquire the force which moves them in the same 
manner and by the same organs, namely, the muscles of 
the arm. An arm the muscles of which are lamed is in- 
capable of doing any work ; the moving force of the 
muscle must be at work in it, and these must obey the 
nerves, which bring to them orders from the brain. 
That member is then capable of the greatest variety of 
motions ; it can compel the most varied instruments to 
execute the most diverse tasks. 

Just so is it with machines : they are used for the most 
diversified arrangements. We produce by their agency 
an infinite variety of movements, with the most various 
degrees of force and rapidity, from powerful steam- 
hammers and rolling-mills, where gigantic masses of iron 
are cut and shaped like butter, to spinning and weaving- 
frames, the work of which rivals that of the spider. 
Modern mechanism has the richest choice of means of 
transferring the motion of one set of rolling wheels to 
another with greater or less velocity ; of changing the 
rotating motion of wheels into the up-and-down motion 


of the piston-rod, of the shuttle, of falling hammers and 
stamps ; or, conversely, of changing the latter into the 
former ; or it can, on the other hand, change move- 
ments of uniform into those of varying velocity, and so 
forth. Hence this extraordinarily rich utility of ma- 
chines for so extremely varied branches of industry. But 
one thing is common to all these differences; they all 
need a 'moving force, which sets and keeps them in 
motion, just as the works of the human hand all need the 
moving force of the muscles. 

Now, the work of the smith requires a far greater and 
more intense exertion of the muscles than that of the 
violin-player; and there are in machines corresponding 
differences in the power and duration of the moving 
force required. These differences, which correspond to 
the different degree of exertion of the muscles in human 
labour, are alone what we have to think of when we 
speak of the amount of work of a machine. We have 
nothing to do here with the manifold character of the 
actions and arrangements which the machines produce ; 
we are only concerned with an expenditure of force. 

This very expression which we use so fluently, ' expen- 
diture of force,' which indicates that the force applied 
has been expended and lost, leads us to a further charac- 
teristic analogy between the effects of the human arm and 
those of machines. The greater the exertion, and the 
longer it lasts, the more is the arm tired, and the more 
is the store of its moving force for the time exhausted. 
\Ve shall see that this peculiarity of becoming exhausted 
by work is also met with in the moving forces of inor- 
ganic nature ; indeed, that this capacity of the human 
arm of being tired is only one of the consequences of the 
law with which we are now concerned. When fatigue 
sets in, recovery is needed, and this can only be effected 
by rest and nourishment. We shall find that also in the 


inorganic moving forces, when their capacity for work is 
spent, there is a possibility of reproduction, although in 
general other means must be used to this end than in the 
case of the human arm. 

From the feeling of exertion and fatigue in our muscles, 
we can form a general idea of what we understand by 
amount of work ; but we must endeavour, instead of the 
indefinite estimate afforded by this comparison, to form a 
clear and precise idea of the standard by which we have 
to measure the amount of work. This we can do better 
by the simplest inorganic moving forces than by the 
actions of our muscles, which are a very complicated 
apparatus, acting in an extremely intricate manner. 

Let us now consider that moving force which we know 
best, and which is simplest gravity. It acts, for ex- 
ample as such, in those clocks which are driven by a 
weight. This weight fastened to a string, which is wound 
round a pulley connected with the first toothed wheel of 
the clock, cannot obey the pull of gravity without setting 
the whole clockwork in motion. Now I must beg you to 
pay special attention to the following points : the weight 
cannot put the clock in motion without itself sinking ; 
did the weight not move, it could not move the clock, 
and its motion can only be such a one as obeys the action 
of gravity. Hence, if the clock is to go, the weight must 
continually sink lower and lower, and must at length sink 
so far that the string which supports it is run out. The 
clock then stops. The useful effect of its weight is for the 
present exhausted. Its gravity is not lost or diminished ; 
it is attracted by the earth as before, but the capacity of 
this gravity to produce the motion of the clockwork is lost. 
It can only keep the weight at rest in the lowest point of 
its path, it cannot farther put it in motion. 

But we can wind up the clock by the power of the arm, 
by which the weight is again raised. When this has been 


done, it has regained its former capacity, and can again 
set the clock in motion. 

We learn from this that a raised weight possesses a 
moving force, but that it must necessarily sink if this 
force is to act ; that by sinking, this moving force is 
exhausted, but by using another extraneous moving force 
that of the arm its activity can be restored. 

The work which the weight has to perform in driving 
the clock is not indeed great. It has continually to 
overcome the small resistances which the friction of the 
axles and teeth, as well as the resistance of the air, oppose 
to the motion of the wheels, and it has to furnish the 
force for the small impulses and sounds which the 
pendulum produces at each oscillation. If the weight is 
detached from the clock, the pendulum swings for a 
while before coming to rest, but its motion becomes each 
moment feebler, and ultimately ceases entirely, being 
gradually used up by the small hindrances I have men- 
tioned. Hence, to keep the clock going, there must be a 
moving force, which, though small, must be continually 
at work. Such a one is the weight. 

We get, moreover, from this example, a measure for the 
amount of work. Let us assume that a clock is driven 
by a weight of a pound, which falls five feet in twenty- 
four hours. If we fix ten such clocks, each with a weight 
of one pound, then ten clocks will be driven twenty-four 
hours ; hence, as each has to overcome the same resistances 
in the same time as the others, ten times as much work 
is performed for ten pounds fall through five feet. Hence, 
we conclude that the height of the fall being the same, 
the work increases directly as the weight. 

Now, if we increase the length of the string so that 
the weight runs down ten feet, the clock will go two 
days instead of one ; and, with double the height of fall, 
the weight will overcome on the second day the same 


resistances as on the first, and will therefore do twice as 
much work as when it can only run down five feet. The 
weight being the same, the work increases as the height 
of fall. Hence, we may take the product of the weight 
into the height of fall as a measure of work, at any rate, 
in the present case. The application of this measure is, 
in fact, not limited to the individual case, but the uni- 
versal standard adopted in manufactures for measuring 
magnitude of work is afoot pound that is, the amount 
of work which a pound raised through a foot can produce. 1 
We may apply this measure of work to all kinds of 
machines, for we should be able to set them all in 
motion by means of a weight sufficient to turn a pulley. 
We could thus always express the magnitude of any 
driving force, for any given machine, by the magnitude 
and height of fall of such a weight as would be necessary 
to keep the machine going with its arrangements until it 
had performed a certain work. Hence it is that the 
measurement of work by foot pounds is universally ap- 
plicable. The use of such a weight as a driving force 
would not indeed be practically advantageous in those 
cases in which we were compelled to raise it by the power 
of our own arm ; it would in that case be simpler to work 
the machine by the direct action of the arm. In the 
clock we use a weight so that we need not stand the whole 
day at the clockwork, as we should have to do to move it 
directly. By winding up the clock we accumulate a store 
of working capacity in it, which is sufficient for the ex- 
penditure of the next twenty-four hours. 

The case is somewhat different when Nature herself 
raises the weight, which then works for us. She does not 
do this with solid bodies, at least not with such regularity 
as to be utilised ; but sae does it abundantly with water, 

1 This is the technical measure of work; to convert it into scientific 
measure it must be multiplied by the intensity of gravity. 



which, being raised to the tops of mountains by meteoro- 
logical processes, returns in streams from them. The 
gravity of water we use as moving force, the most direct 
application being in what are called overshot wheels, one 
of which is represented in Fig. 38. Along the circumfer- 
ence of such a wheel are a series of buckets, which act as 

FIG. 38. 

receptacles for the water, and, on the side turned to the 
observer, have the tops uppermost ; on the opposite side 
the tops of the buckets are upside-down. The water flows 
at M into the buckets of the front of the wheel, and at 
F, where the mouth begins to incline downwards, it flows 
out. The buckets on the circumference are filled on the 


side turned to the observer, and empty on the other side. 
Thus the former are weighted by the water contained in 
them, the latter not ; the weight of the water acts con- 
tinuously on only one side of the wheel, draws this down, 
and thereby turns the wheel ; the other side of the wheel 
offers no resistance, for it contains no water. It is thus 
the weight of the falling water which turns the wheel, 
and furnishes the motive power. But you will at once see 
that the mass of water which turns the wheel must neces- 
sarily fall in order to do so, and that though, when it 
has reached the bottom, it has lost none of its gravity, it 
is no longer in a position to drive the wheel, if it is not 
restored to its original position, either by the power of 
the human arm or by means of some other natural force. 
If it can flow from the mill-stream to still lower levels, 
it may be used to work other wheels. But when it has 
reached its lowest level, the sea, the last remainder of 
the moving force is used up, which is due to gravity - 
that is, to the attraction of the earth, and it cannot act 
by its weight until it has been again raised to a high level. 
As this is actually effected by meteorological processes, 
you will at once observe that these are to be considered as 
sources of moving force. 

Water-power was the first inorganic force which man 
learnt to use instead of his own labour or of that of domes- 
tic animals. According to Strabo, it was known to King 
Mithridates, of Pontus, who was also otherwise celebrated 
for his knowledge of nature ; near his palace there was a 
water-wheel. Its use was first introduced among the 
Romans in the time of the first Emperors. Even now we 
find water-mills in all mountains, valleys, or wherever 
there are rapidly-flowing, regularly-filled, brooks and 
streams. We find water-power used for all purposes which 
>ean possibly be effected by machines. It drives mills 
which grind corn, saw-mills, hammers and oil-presses, 


spinning-frames and looms, and so forth. It is the 
cheapest of all motive powers, it flows spontaneously 
from the inexhaustible stores of nature ; but it is re- 
stricted to a particular place, and only in mountainous 
countries is it present in any quantity ; in level countries 
extensive reservoirs are necessary for damming the rivers 
to produce any amount of water-power. 

Before passing to the discussion of other motive forces, 
I must answer an objection which may readily suggest 
itself. We all know that there are numerous machines, 
systems of pulleys, levers and cranes, by the aid of which 
heavy burdens may be lifted by a comparatively small 
expenditure of force. We have all of us often seen one or 
two workmen hoist heavy masses of stones to great heights, 
which they would be quite unable to do directly ; in like 
manner, one or two men, by means of a crane, can trans- 
fer the largest and heaviest chests from a ship to the quay. 
Now it may be asked, If a large, heavy weight had been 
used for driving a machine, would it not be very easy, by 
means of a crane or a system of pulleys, to raise it anew, 
so that it could again be used as a motor, and thus acquire 
motive power, without being compelled to use a corre- 
sponding exertion in raising the weight ? 

The answer to this is, that all these machines, in that 
degree in which for the moment they facilitate the exer- 
tion, also prolong it, so that by their help no motive power 
is ultimately gained. Let us assume that four labourers 
have to raise a load of four hundredweight, by means of 
a rope passing over a single pulley. Every time the rope 
is pulled down through four feet, the load is also raised 
through four feet. But now, for the sake of comparison, 
let us suppose the same load hung to a block of four 
pulleys, as represented in Fig. 39. A single labourer 
would now be able to raise the load by the same exertion 
of force as each one of the four put forth. But when he 



Fio. 39. 

pulls the rope through four feet, the load only rises one 

foot, for the length through which he pulls the rope, at a, is 

uniformly distributed in the block over four ropes, so that 

each of these is only shortened 

by a foot. To raise the load, 

therefore, to the same height, 

the one man must necessarily 

vvork four times as long as the 

four together did. But the total 

expenditure of work is the same, 

whether four labourers work for 

a quarter of an hour or one works 

for an hour. 

If, instead of human labour, 
we introduce the work of a 
weight, and hang to the block a 
load of 400, and at a, where 
otherwise the labourer works, a 
weight of 100 pounds, the block 
is then in equilibrium, and, 
without any appreciable exer- 
tion of the arm, may be set in 
motion. The weight of 100 
pounds sinks, that of 400 rises. 
Without any measurable expen- 
diture of force, the heavy weight 
has been raised by the sinking 
of the smaller one. But observe 
that the smaller weight will 
have sunk through four times 
the distance that the greater 

one has risen. But a fall of 100 pounds through four 
feet is just as much 400 foot pounds as a fall of 400 pounds 
through one foot. 

The action of levers in all their various modifications 


is precisely similar. Let a b, Fig. 40, be a simple lever, 
supported at c, the arm c b being four times as long as the 
other arm a c. Let a weight of one pound be hung at 6, 
and a weight of four pounds at a, the lever is then in equi- 
librium, and the least pressure of the finger is sufficient, 
without any appreciable exertion of force, to place it in 
the position of &', in which the heavy weight of four 
pounds has been raised, while the one-pound weight has 
sunk. But here, also, you will observe no work has 
been gained, for while the heavy weight has been raised 

Fia. 40. 

through one inch, the lighter one has fallen through 
four inches ; and four pounds through one inch is, as work, 
equivalent to the product of one pound through four 

Most other fixed parts of machines may be regarded as 
modified and compound levers ; a toothed-wheel, for in- 
stance as a series of levers, the ends of which are repre- 
sented by the individual teeth, and one after the other of 
which is put in activity, in the degree in which the 
tooth in question seizes, or is seized by the adjacent 
pinion. Take, for instance, the crabwinch, represented in 
Fig. 41. Suppose the pinion on the axis of the barrel of 


the winch has twelve teeth, and the toothed-wheel, H H, 
seventy-two teeth, that is six times as many as the 
former. The winch must now be turned round six times 
before the toothed-wheel, H, and the barrel, D, have 
made one turn, and before the rope which raises the load 
has been lifted by a length equal to the circumference of 
the barrel. The workman thus requires six times the 

FIG. 41. 

time, though to be sure only one-sixth of the exertion, 
which he would have to use if the handle were directly 
applied to the barrel, D. In all these machines, and parts 
of machines, we find it confirmed that in proportion as 
the velocity of the motion increases its power diminishes, 
and that when the power increases the velocity diminishes, 
but that the amount of work is never thereby increased. 

In the overshot mill-wheel, described above, water acts 
by its weight. But there is another form of mill-wheels, 



what is called the undershot wheel, in which it only acts 
by its impact, as represented in Fig. 42. These are used 
where the height from which the water comes is not great 
enough to flow on the upper part of the wheel. The 
lower part of undershot wheels dips in the flowing water 
which strikes against their float-boards and carries them 
along. Such wheels are used in swift-flowing streams 
which have a scarcely perceptible fall, as, for instance, on 

FIG. 42. 

the Rhine. In the immediate neighbourhood of such a 
wheel, the water need not necessarily have a great fall it 
it only strikes with considerable velocity. It is the velo- 
city of the water, exerting an impact against the float- 
boards, which acts in this case, and which produces the 
motive power. 

Windmills, which are used in the great plains of Holland 
and North Germany to supply the want of falling water, 
afford another instance of the action of velocity. The 


sails are driven by air in motion by wind. Air at rest 
could just as little drive a windmill as water at rest a 
water-wheel. The driving force depends here on the 
velocity of moving masses. 

A bullet resting in the hand is the most harmless thing 
in the world ; by its' gravity it can exert no great effect : 
but when fired and endowed with great velocity it drives 
through all obstacles with the most tremendous force. 

If I lay the head of a hammer gently on a nail, neither 
its small weight nor the pressure of my arm is quite 
sufficient to drive the nail into wood ; but if I swing the 
hammer and allow it to fall with great velocity, it 
acquires a new force, which can overcome far greater 

These examples teach us that the velocity of a moving 
mass can act as motive force. In mechanics, velocity in 
so far as it is motive force, and can produce work, is 
called vis viva. The name is not well chosen ; it is too 
apt to suggest to us the force of living beings. Also in 
this case you will see, from the instances of the hammer 
and of the bullet, that velocity is lost as such, when it 
produces working power. In the case of the water-mill, 
or of the windmill, a more careful investigation of the 
moving masses of water and air is necessary to prove that 
part of their velocity has been lost by the work which 
they have performed. 

The relation of velocity to working power is most 
simply and clearly seen in a simple pendulum, such as can 
be constructed by any weight which we suspend to a cord. 
Let M, Fig. 43, be such a weight, of a spherical form ; A B, 
a horizontal line drawn through the centre of the sphere ; 
P the point at which the cord is fastened. If now I draw 
the weight M on one side towards A, it moves in the arc 
M a, the end of which, a, is somewhat higher than the 
point A in the horizontal line. The weight is thereby 



raised to the height A a. Hence my arm must exert a 
certain force to bring the weight to a. Gravity resists 
this motion and endeavours to bring back the weight to 
M, the lowest point which it can reach. 

Now, if after I have brought the weight to a I let it 
go, it obeys this force of gravity and returns to M, arrives 
there with a certain velocity, and no longer remains 
quietly hanging at M as it did before, but STK ings be- 

FIG. 43. 

yond M towards 6, where its motion stops as soon as it 
has traversed on the side of B an arc equal in length to 
that on the side of A, and after it has risen to a distance 
B b above the horizontal line, which is equal to the height 
A a, to which my arm had previously raised it. In b the 
pendulum returns, swings the same way back through M 
towards a, and so on, until its oscillations are gradually 
diminished, and ultimately annulled by the resistance of 
the air and by friction. 


You see here that the reason why the weight, when it 
comes from a to M, and does not stop there, but ascends 
to 6, in opposition to the action of gravity, is only to be 
sought in its velocity. The velocity which it has ac- 
quired in moving from the height A a is capable of again 
raising it to an equal height, B 6. The velocity of the 
moving mass, M, is thus capable of raising this mass ; 
that is to say, in the language of mechanics, of performing 
work. This would also be the case if we had imparted 
such a velocity to the suspended weight by a blow. 

From this we learn further how to measure the workin g 
power of velocity or, what is the same thing, the vis 
viva of the moving mass. It is equal to the work, 
expressed in foot pounds, which the same mass can 
exert after its velocity has been used to raise it, under 
the most favourable circumstances, to as great a height 
as possible. 1 This does not depend on the direction of 
the velocity; for if we swing a weight attached to a 
thread in a circle, we can even change a downward 
motion into an upward one. 

The motion of the pendulum shows us very distinctly 
how the forms of working power hitherto considered 
that of a raised weight and that of a moving mass may 
merge into one another. In the points a and 6, Fig. 43, 
the mass has no velocity ; at the point M it has fallen as 
far as possible, but possesses velocity. As the weight goes 
from a to m the work of the raised weight is changed into 
vis viva ; as the weight goes further from m to b the vis 
viva is changed into the work of a raised weight. Thus the 
work which the arm originally imparted to the pendulum 
is not lost in these oscillations, provided we may leave out 
of consideration the influence of the resistance of the air 

1 The measure of vis viva in theoretical mechanics is half the product of 
the weight into the square of the velocity. To reduce it to the technical 
measure of the work we must divide it by the intensity of gravity ; that 
is, by the velocity at the end of the first second of a freely falling body. 


and of friction. Neither does it increase, but it continually 
changes the form of its manifestation. 

Let us now pass to other mechanical forces, those 
of elastic bodies. Instead of the weights which drive 
our clocks, we find in time-pieces and in watches, steel 
springs which are coiled in winding up the clock, and 
are uncoiled by the working of the clock. To coil up the 
spring we consume the force of the arm ; this has to 
overcome the resisting elastic force of the spring as we 
wind it up, just as in the clock we have to overcome the 
force of gravity which the weight exerts. The coiled 
spring can, however, perform work ; it gradually expends 
this acquired capability in driving the clockwork. 

If I stretch a crossbow and afterwards let it go, the 
stretched string moves the arrow ; it imparts to it force 
in the form of velocity. To stretch the cord my arm 
must work for a few seconds ; this work is imparted 
to the arrow at the moment it is shot off. Thus the 
crossbow concentrates into an extremely short time 
the entire work which the arm had communicated in the 
operation of stretching; the clock, on the contrary, 
spreads it over one or several days. In both cases no 
work is produced which my arm did not originally impart 
to the instrument, it is only expended more conveniently. 

The case is somewhat different if by any other natural 
process I can place an elastic body in a state of tension 
without having to exerii my arm. This is possible and 
is most easily observed in the case of gases. 

If, for instance, I discharge a fire-arm loaded \vith 
gunpowder, the greater part of the mass of the powder is 
converted into gases at a very high temperature, which 
have a powerful tendency to expand, and can only be 
retained in the narrow space in which they are formed, 
by the exercise of the most powerful pressure. In 
expanding with enormous force they propel the bullet, 



and impart to it a great velocity, which we have already 
seen is a form of work. 

In this case, then, I have gained work which my arm 
has not performed. Something, however, has been lost ; 
the gunpowder, that is to say, whose constituents have 
changed into other chemical compounds, from which 
they cannot, without further ado, be restored to their 
original condition. Here, then, a chemical change has 
taken place, under the influence of which work has been 

Elastic forces are produced in gases by the aid of heat, 
on a far greater scale. 

Let us take, as the most simple instance, atmospheric 
air. In Fig. 44 an apparatus is represented such as 

FIG. 44. 

Kegnault used for measuring the expansive force of heated 
gases. If no great accuracy is required in the measure- 


ment, the apparatus may be arranged more simply. At 
C is a glass globe rilled with dry air, which is placed in 
a metal vessel, in which it can be heated by steam. It is 
connected with the U-shaped tube, s s, which contains a 
liquid, and the limbs of which communicate with each 
other when the stop-cock R is closed. If the liquid is in 
equilibrium in the tube ss when the globe is cold, it 
rises in the leg s, and ultimately overflows when the 
globe is heated. If, on the contrary, when the globe is 
heated, equilibrium be restored by allowing some of the 
liquid to flow out at K, as the globe cools it will be drawn 
up towards n. In both cases liquid is raised, and work 
thereby produced. 

The same experiment is continuously repeated on the 
largest scale in steam engines, though in order to keep 
up a continual disengagement of compressed gases from 
the boiler, the air in the globe in Fig. 44, which would 
soon reach the maximum of its expansion, is replaced by 
water, which is gradually changed into steam by the 
application of heat. But steam, so long as it remains 
as such, is an elastic gas which endeavours to expand 
exactly like atmospheric air. And instead of the column 
of liquid which was raised in our last experiment, the 
machine is caused to drive a solid piston which imparts 
its motion to other parts of the machine. Fig. 45 re- 
presents a front view of the working parts of a high 
pressure engine, and Fig. 46 a section. The boiler in 
which steam is generated is not represented ; the steam 
passes through the tube z z, Fig. 46, to the cylinder A A, 
in which moves a tightly fitting piston c. The parts 
between the tube z z and the cylinder A A, that is the 
slide valve in the valve-chest K K, and the two tubes d 
and e allow the steam to pass first below and then above 
the piston, while at the same time the steam has free 
exit from the other half of the cylinder. When the 


Fio. 45. 


Fio. 46. 




steam passes under the piston, it forces it upward ; when 
the piston has reached the top of its course the position 
of the valve in KK 'changes, and the steam passes above 
the piston and forces it down again. The piston-rod acts 
by means of the connecting-rod p, on the crank Q of the 
fly-wheel x and sets this in motion. By means of the 
rod s, the motion of the rod regulates the opening and 
closing of the valve. But we need not here enter into 
those mechanical arrangements, however ingeniously they 
have been devised. We are only interested in the manner 
in which heat produces elastic vapour, and how this 
vapour, in its endeavour to expand, is compelled to move 
the solid parts of the machine, and furnish work. 

You all know how powerful and varied are the effects 
of which steam engines are capable ; with them has 
really begun the great development of industry which 
has characterised our century before all others. Its 
most essential superiority over motive powers formerly 
known, is that it is not restricted to a particular place. 
The store of coal and the small quantity of water 
which are the sources of its power can be brought 
everywhere, and steam engines can even be made mov- 
able, as is the case with steam-ships and locomotives. 
By means of these machines we can develope motive 
power to almost an indefinite extent at any place on the 
earth's surface, in deep mines and even on the middle 
of the ocean ; while water and wind-mills are bound to 
special parts of the surface of the land. The locomotive 
transports travellers and goods over the land in numbers 
and with a speed which must have seemed an incredible 
fable to our forefathers, who looked upon the mail- 
coach with its six passengers in the inside and its ten 
miles an hour, as an enormous progress. Steam-engines 
traverse the ocean independently of the direction of the 
wind, and, successfully resisting storms which would drive 


sailing-vessels far away, reach their goal at the appointed 
time. The advantages which the concourse of numerous, 
and variously skilled workmen in all branches offers in 
large towns where wind and water power are wanting, can 
be utilised, for steam-engines find place everywhere, 
and supply the necessary crude force ; thus the more in- 
telligent human force may be spared for better purposes ; 
and, indeed, wherever the nature of the ground or the 
neighbourhood of suitable lines of communication present 
a favourable opportunity for the development of industry, 
the motive power is also present in the form of steam- 

We see, then, that heat can produce mechanical power ; 
but in the cases which we have discussed we have seen 
that the quantity of force which can be produced by a 
given measure of a physical process is always accurately 
defined, and that the further capacity for work of the 
natural forces, is either diminished or exhausted by the 
work which has been performed. How is it now with Heat 
in this respect ? 

This question was of decisive importance in the en- 
deavour to extend the law of the Conservation of Force 
to all natural processes. In the answer lay the chief 
difference between the older and newer views in these 
respects. Hence it is that many physicists designate 
that view of Nature corresponding to the law of the 
conservation of force with the name of the Mechanical 
Theory of Heat. 

The older view of the nature of heat was that it is a 
substance, very fine and imponderable indeed, but in- 
destructible, and unchangeable in quantity, which is an 
essential fundamental property of all matter. And, in 
fact, in a large number of natural processes, the quantity 
of heat which can be demonstrated by the thermometer 
is unchangeable. 


By conduction and radiation, it can indeed pass from 
hotter to colder bodies ; but the quantity of heat which 
the former lose can be shown by the thermometer to have 
reappeared in the latter. Many processes, too, were 
known, especially in the passage of bodies from the solid 
to the liquid and gaseous states, in which heat dis- 
appeared at any rate, as regards the thermometer. But 
when the gaseous body was restored to the liquid, and the 
liquid to the solid state, exactly the same quantity of heat 
reappeared which formerly seemed to have been lost. 
Heat was said to have become latent. On this view, liquid 
water differed from solid ice in containing a certain 
quantity of heat bound, which, just because it was bound, 
could not pass to the thermometer, and therefore was not 
indicated by it. Aqueous vapour contains a far greater 
quantity of heat thus bound. But if the vapour be pre- 
cipitated, and the liquid water restored to the state of 
ice, exactly the same amount of heat is liberated as had 
become latent in the melting of the ice and in the 
vaporisation of the water. 

Finally, heat is sometimes produced and sometimes 
disappears in chemical processes. But even here it might 
be assumed that the various chemical elements and 
chemical compounds contain certain constant quantities 
of latent heat, which, when they change their composi- 
tion, are sometimes liberated and sometimes must be 
supplied from external sources. Accurate experiments 
have shown that the quantity of heat which is developed 
by a chemical process, for instance, in burning a pound 
of pure carbon into carbonic acid, is perfectly con- 
stant, whether the combustion is slow or rapid, whether 
it takes place all at once or by intermediate stages. This 
also agreed very well with the assumption, which was the 
basis of the theory of heat, that heat is a substance 
entirely unchangeable in quantity. The natural processes 


which have here been briefly mentioned, were the subject 
of extensive experimental and mathematical investiga- 
tions, especially of the great French physicists in the 
last decade of the former, and the first decade of the 
present, century ; and a rich and accurately-worked chapter 
of physics had been developed, in which everything agreed 
excellently with the hypothesis that heat is a substance. 
On the other hand, the invariability in the quantity of 
heat in all these processes could at that time be explained 
in no other manner than that heat is a substance. 

But one relation of heat namely, that to mechanical 
work had not been accurately investigated. A French 
engineer, Sadi Carnot, son of the celebrated War Minister 
of the Revolution, had indeed endeavoured to deduce the 
work which heat performs, by assuming that the hypo- 
thetical caloric endeavoured to expand like a gas ; and 
from this assumption he deduced in fact a remarkable 
law as to the capacity of heat for work, which even now, 
though with an essential alteration introduced by Clausius, 
is among the bases of the modern mechanical theory of 
heat, and the practical conclusions from which, so far as 
they could at that time be compared with experiments, 
have held good. 

But it was already known that whenever two bodies 
in motion rubbed against each other, heat was developed 
anew, and it could not be said whence it came. 

The fact is universally recognised ; the axle of a car- 
riage which is badly greased and where the friction is 
great, becomes hot so hot, indeed, that it may take fire ; 
machine-wheels with iron axles going at a great rate may 
become so hot that they weld to their sockets. A power- 
ful degree of friction is not, indeed, necessary to disen- 
gage an appreciable degree of heat ; thus, a lucifer- 
match, which by rubbing is so heated that the phosphoric 
mass ignites, teaches this fact. Nay, it is enough to rub 


the dry hands together to feel the heat produced by fric- 
tion, and which is far greater than the heating which 
takes place when the hands lie gently on each other. 
Uncivilized people use the friction of two pieces of wood 
to kindle a fire. With this view, a sharp spindle of hard 
wood is made to revolve rapidly on a base of soft wood in 
the manner represented in Fig. 47. 

FIG. 47. 

So long as it was only a question of the friction of 
solids, in which particles from the surface become de- 
tached and compressed, it might be supposed that some 
changes in structure of the bodies rubbed might here 
liberate latent heat, which would thus appear as heat of 

But heat can also be produced by the friction of liquids, 
in which there could be no question of changes in struc- 
ture, or of the liberation of latent heat. The first de- 
cisive experiment of this kind was made by Sir Humphry 
Davy in the commencement of the present century. Jn 


a cooled space lie made two pieces of ice rub against each 
other, and thereby caused them to melt. The latent heat 
which the newly formed water must have here assimilated 
could not have been conducted to it by the cold ice, or 
have been produced by a change of structure ; it could 
have come from no other cause than from friction, and 
must have been created by friction. 

Heat can also be produced by the impact of imperfectly 
elastic bodies as well as by friction. This is the case, for 
instance, when we produce fire by striking flint against 
steel, or when an iron bar is worked for some time by 
powerful blows of the hammer. 

If we inquire into the mechanical effects of friction 
and of inelastic impact, we find at once that these are 
the processes by which all terrestrial movements are 
brought to rest. A moving body whose motion was not 
retarded by any resisting force would continue to move to 
all eternity. The motions of the planets are an instance 
of this. This is apparently never the case with the mo- 
tion of the terrestrial bodies, for they are always in con- 
tact with other bodies which are at rest, and rub against 
them. We can, indeed, very much diminish their fric- 
tion, but never completely annul it. A wheel which turns 
about a well-worked axle, once set in motion continues 
it for a long time ; and the longer, the more truly and 
smoother the axle is made to turn, the better it is greased, 
and the less the pressure it has to support. Yet the vis 
viva of the motion which we have imparted to such a 
wheel when we started it, is gradually lost in consequence 
of friction. It disappears, and if we do not carefully 
consider the matter, it seems as if the vis viva which the 
wheel had possessed had been simply destroyed without 
any substitute. 

A bullet which is rolled on a smooth horizontal surface 
continues to roll until its velocity is destroyed by fric- 


tion on the path, caused by the very minute impacts 
on its little roughnesses. 

A pendulum which has been put in vibration can con- 
tinue to oscillate for hours if the suspension is good, 
without being driven by a weight ; but by the friction 
against the surrounding air, and by that at its place of 
suspension, it ultimately comes to rest. 

A stone which has fallen from a height has acquired a 
certain velocity on reaching the earth ; this we know is the 
equivalent of a mechanical work ; so long as this velocity 
continues as such, we can direct it upwards by means of 
suitable arrangements, and thus utilise it to raise the 
stone again. Ultimately the stone strikes against the 
earth and comes to rest ; the impact has destroyed its 
velocity, and therewith apparently also the mechanical 
work which this velocity could have effected. 

If we review the result of all these instances, which 
each of you could easily add to from your own daily ex- 
perience, we shall see that friction and inelastic impact 
are processes in which mechanical work is destroyed, and 
heat produced in its place. 

The experiments of Joule, which have been already 
mentioned, lead us a step further. He has measured in 
foot pounds the amount of work which is destroyed by the 
friction of solids and by the friction of liquids ; and, on 
the other hand, he has determined the quantity of heat 
which is thereby produced, and has established a definite 
relation between the two. His experiments show that 
when heat is produced by the consumption of work, a 
definite quantity of work is required to produce that 
amount of heat which is known to physicists as the unit 
of heat ; the heat, that is to say, which is necessary to 
raise one gramme of water through one degree centigrade. 
The quantity of wcrk necessary for this is, according to 
Joule's best experiments, equal to the work which a 


gramme would perform in falling through a height of 
425 metres. 

In order to show how closely concordant are his 
numbers, I will adduce the results of a few series of 
experiments which he obtained after introducing the 
latest improvements in his methods. 

1. A series of experiments in which water was heated 
by friction in a brass vessel. In the interior of this 
vessel a vertical axle provided with sixteen paddles was 
rotated, the eddies thus produced being broken by a series 
of projecting barriers, in which parts were cut out large 
enough for the paddles to pass through. The value of 
the equivalent was 424-9 metres. 

2. Two similar experiments, in which mercury in an 
iron vessel was substituted for water in a brass one, gave 
425 and 426-3 metres. 

3. Two series of experiments, in which a conical ring 
rubbed against another, both surrounded by mercury, 
gave 426-7 and 425-6 metres. 

Exactly the same relations between heat and work 
were also found in the reverse process that is, when 
work was produced by heat. In order to execute this 
process under physical conditions that could be controlled 
as perfectly as possible, permanent gases and not vapours 
were used, although the latter are, in practice, more con- 
venient for producing large quantities of work, as in the 
case of the steam-engine. A gas which is allowed to 
expand with moderate velocity becomes cooled. Joule 
was the first to show the reason of this cooling. For the 
gas has, in expanding, to overcome the resistance, which 
the pressure of the atmosphere and the slowly yielding 
side of the vessel oppose to it ; or, if it cannot of itself 
overcome this resistance, it supports the arm of the 
observer which does it. Gas thus performs work, and 
this work is produced at the cost of its heat. Hence the 


cooling. If, on the contrary, the gas is suddenly allowed 
to issue into a perfectly exhausted space where it finds no 
resistance, it does not become cool as Joule has shown ; 
or if individual parts of it become cool, others become 
warm ; and, after the temperature has become equalised, 
this is exactly as much as before the sudden expansion of 
the gaseous mass. 

How much heat the various gases disengage when they 
are compressed, and how much work is necessary for their 
compression ; or, conversely, how much heat disappears 
when they expand under a pressure equal to their own 
counterpressure, and how much work they thereby effect in 
overcoming this counterpressure, was partly known from 
the older physical experiments, and has partly been de- 
termined by the recent experiments of Eegnault by 
extremely perfect methods. Calculations with the best 
data of this kind give us the value of the thermal equiva- 
lent from experiments : 

With atmospheric air 426-0 metres. 

oxygen . . . . . . 4257 

,, nitrogen . . . . . 431*3 

hydrogen ... . 4 25 '3 

Comparing these numbers with those which determine 
the equivalence of heat and mechanical work in friction, 
as close an agreement is seen as can at all be expected 
from numbers which have been obtained by such varied 
investigations of different observers. 

Thus then : a certain quantity of heat may be changed 
into a definite quantity of work ; this quantity of work can 
also be retransformed into heat, and, indeed, into exactly 
the same quantity of heat as that from which it origi- 
nated ; in a mechanical point of view, they are exactly 
equivalent. Heat is a new form in which a quantity of 
work may appear. 

These facts no longer permit us to regard heat as a 


substance, for its quantity is not unchangeable. It can 
be produced anew from the vis viva of motion destroyed ; 
it can be destroyed, and then produces motion. We must 
rather conclude from this that heat itself is a motion, an 
internal invisible motion of the smallest elementary par- 
ticles of bodies. If, therefore, motion seems lost in 
friction and impact, it is not actually lost, but only passes 
from the great visible masses to their smallest particles ; 
while in steam-engines the internal motion of the heated 
gaseous particles is transferred to the piston of the 
machine, accumulated in it, and combined in a resultant 

But what is the nature of this internal motion, can only 
be asserted with any degree of probability in the case of 
gases. Their particles probably cross one another in 
rectilinear paths in all directions, until, striking another 
particle, or against the side of the vessel, they are re- 
flected in another direction. A gas would thus be 
analogous to a swarm of gnats, consisting, however, of 
particles infinitely small and infinitely more closely 
packed. This hypothesis, which has been developed by 
Kronig, Clausius, and Maxwell, very well accounts for all 
the phenomena of gases. 

What appeared to the earlier physicists to be the con- 
stant quantity of heat is nothing more than the whole 
motive power of the motion of heat, which remains con- 
stant so long as it is not transformed into other forms of 
work, or results afresh from them. 

We turn now to another kind of natural forces which 
can produce work I mean the chemical. We have to- 
day already come across them. They are the ultimate 
cause of the work which gunpowder and the steam-engine 
produce ; for the heat which is consumed in the latter, 
for example, originates in the combustion of carbon 
that is to say, in a chemical process. The burning of 


coal is the chemical union of carbon with the oxygen of 
the air, taking place under the influence of the chemical 
affinity of the two substances. 

We may regard this force as an attractive force between 
the two, which, however, only acts through them with 
extraordinary power, if the smallest particles of the two 
substances are in closest proximity to each other. In 
combustion this force acts ; the carbon and oxygen atoms 
strike against each other and adhere firmly, inasmuch as 
they form a new compound carbonic acid a gas known 
to all of you as that which ascends from all fermenting 
and fermented liquids from beer and champagne. Now 
this attraction between the atoms of carbon and of oxygen 
performs work just as much as that which the earth in the 
form of gravity exerts upon a raised weight. When the 
weight falls to the ground, it produces an agitation, which 
is partly transmitted to the vicinity as sound waves, and 
partly remains as the motion of heat. The same result 
we must expect from chemical action. When carbon and 
oxygen atoms have rushed against each other, the newly- 
formed particles of carbonic acid must be in the most 
violent molecular motion that is, in the motion of heat. 
And this is so. A pound of carbon burned with oxygen to 
form carbonic acid, gives as much heat as is necessary to 
raise 80-9 pounds of water from the freezing to the 
boiling point ; and just as the same amount of work is 
produced when a weight falls, whether it falls slowly or 
fast, so also the same quantity of heat is produced by the 
combustion of carbon, whether this is slow or rapid, 
whether it takes place all at once, or by successive stages 

When the carbon is burned, we obtain in its stead, ana 
in that of the oxygen, the gaseous product of combustion 
carbonic acid. Immediately after combustion it is in- 
candescent. When it has afterwards imparted heat to the 
vicinity, we have in the carbonic acid the entire quantity 


of carbon and the entire quantity of oxygen, and also the 
force of affinity quite as strong as before. But the action 
of the latter is now limited to holding the atoms of 
carbon and oxygen firmly united; they can no longer 
produce either heat or work any more than a fallen 
weight can do work if it has not been again raised 
by some extraneous force. When the carbon has been 
burnt we take no further trouble to retain the car- 
bonic acid ; it can do no more service, we endeavour 
to get it out of the chimneys of our houses as fast as we 

Is it possible, then, to tear asunder the particles of 
carbonic acid, and give to them once more the capacity of 
work which they had before they were combined, just as 
we can restore the potentiality of a weight by raising it 
from the ground? It is indeed possible. We shall after- 
wards see how it occurs in the life of plants ; it can also 
be effected by inorganic processes, though in roundabout 
ways, the explanation of which would lead us too far from 
our present course. 

This can, however, be easily and directly shown for 
another element, hydrogen, which can be burnt just like 
carbon. Hydrogen with carbon is a constituent of all 
combustible vegetable substances, among others, it is also 
an essential constituent of the gas which is used for 
lighting our streets and rooms; in the free state it is 
also a gas, the lightest of all, and burns when ignited 
with a feebly luminous blue flame. In this combustion 
that is, in the chemical combination of hydrogen with 
oxygen, a very considerable quantity of heat is produced ; 
for a given weight of hydrogen, four times as much heat 
as in the combustion of the same weight of carbon. The 
product of combustion is water, which, therefore, is not of 
itself further combustible, for the hydrogen in it is com- 
pletely saturated with oxygen. The force of affinity, 


therefore, of hydrogen for oxygen, like that of carbon for 
oxygen, performs work in combustion, which appears in 
the form of heat. In the water which has been formed 
during combustion, the force of affinity is exerted between 
the elements as before, but its capacity for work is lost. 
Hence the two elements must be again separated, their 
atoms torn apart, if new effects are to be produced from 

This we can do by the aid of currents of electricity. 
In the apparatus depicted in Fig. 48, we have two glass 

FIG. 48. 


vessels filled with acidulated water, a and a 1 , which are 
separated in the middle by a porous plate moistened with 
water. In both sides are fitted platinum wires, k, which 
are attached to platinum plates, i and i 1 . As soon as a 
galvanic current is transmitted through the water by the 
platinum wires, k, you see bubbles of gas ascend from 
the plates i and i 1 . These bubbles are the two elements 
of water, hydrogen on the one hand, and oxygen on the 
other. The gases emerge through the tubes g and g 1 . 
If we wait until the upper part of the vessels and the 
tubes have been filled with it, we can inflame hydrogen 
at one side ; it burns with a blue flame. If I bring a 
glimmering spill near the mouth of the other tube it 



bursts into flame, just as happens with oxygen gas, in 
which the processes of combustion are far more intense 
than in atmospheric air, where the oxygen mixed with 
nitrogen is only one-fifth of the whole volume. 

If I hold a glass flask filled with water over the hydro- 
gen flame, the water, newly formed in combustion, con- 
denses upon it. 

If a platinum wire be held in the almost non-luminous 
flame, you see how intensely it is ignited ; in a plentiful 
current of a mixture of the gases, hydrogen and oxygen, 
which have been liberated in the above experiment, the 

FIG. 49. 

almost infusible platinum might even be melted. The 
hydrogen which has here been liberated from the water 
by the electrical current has regained the capacity of 
producing large quantities of heat by a fresh combination 
with oxygen ; its affinity for oxygen has regained for it 
its capacity for work. 

We here become acquainted with a new source of 
work, the electric current which decomposes water. This 
current is itself produced by a galvanic battery, Fig. 49. 


Each of the four vessels contains nitric acid, in which 
there is a hollow cylinder of very compact carbon. In 
the middle of the carbon cylinder is a cylindrical porous 
vessel of white clay, which contains dilute sulphuric acid ; 
in this dips a zinc cylinder. Each zinc cylinder is con- 
nected by a metal ring with the carbon cylinder of the 
next vessel, the last zinc cylinder n is connected with one 
platinum plate, and the first carbon cylinder, p, with the 
other platinum plate of the apparatus for the decomposi- 
tion of water. 

If now the conducting circuit of this galvanic appa- 
ratus is completed, and the decomposition of water begins, 
a chemical process takes place simultaneously in the cells 
of the voltaic battery. Zinc takes oxygen from the sur- 
rounding water and undergoes a slow combustion. The 
product of combustion thereby produced, oxide of zinc, 
unites further with sulphuric acid, for which it has a 
powerful affinity, and sulphate of zinc, a saline kind of 
substance, dissolves in the liquid. The oxygen, moreover, 
which is withdrawn from it is taken by the water from 
the nitric acid surrounding the cylinder of carbon, which 
is very rich in it, and readily gives it up. Thus, in the 
galvanic battery zinc burns to sulphate of zinc at the cost 
of the oxygen of nitric acid. 

Thus, while one product of combustion, water, is again 
separated, a new combustion is taking place that of 
zinc. While we there reproduce chemical affinity which 
is capable of work, it is here lost. The electrical current 
is, as it were, only the carrier which transfers the chemical 
force of the zinc uniting with oxygen and acid to water 
in the decomposing cell, and uses it for overcoming the 
chemical force of hydrogen and oxygen. 

In this case, we can restore work which has been lost, 
but only by using another force, that of oxidising zinc. 

Here we have overcome chemical forces by chemical 



forces, through the instrumentality of the electrical cur- 
rent. But we can attain the same object by mechanical 

FIG. 50. 

forces, if we produce the electrical current by a magneto- 
electrical machine, Fig. 50. If we turn the handle, the 
anker R R 1 , on which is coiled copper-wire, rotates in front 


of the poles of the horse-shoe magnet, and in these coils 
electrical currents are produced, which can be led from 
the points a and b. If the ends of these wires are con- 
nected with the apparatus for decomposing water we 
obtain hydrogen and oxygen, though in far smaller quan- 
tity than by the aid of the battery which we used before. 
But this process is interesting, for the mechanical force 
of the arm which turns the wheel produces the work which 
is required for separating the combined chemical ele- 
ments. Just as the steam-engine changes chemical into 
mechanical force, the magneto-electrical machine trans- 
forms mechanical force into chemical. 

The application of electrical currents opens out a large 
number of relations between the various natural forces. 
We have decomposed water into its elements by such 
currents, and should be able to decompose a large number 
of other chemical compounds. On the other hand, in 
ordinary galvanic batteries electrical currents are produced 
by chemical forces. 

In all conductors through which electrical currents 
pass they produce heat ; I stretch a thin platinum wire 
between the ends n and p of the galvanic battery, Fig. 49 ; 
it becomes ignited and melts. On the other hand, elec- 
trical currents are produced by heat in what are called 
thermo-electric elements. 

Iron which is brought near a spiral of copper wire, 
traversed by an electrical current, becomes magnetic, 
and then attracts other pieces of iron, or a suitably 
placed steel magnet. We thus obtain mechanical actions 
which meet with extended applications in the electrical 
telegraph, for instance. Fig. 51 represents a Morse's 
telegraph in one-third of the natural size. The essential 
part is a horse-shoe shaped iron core, which stands in the 
copper spirals b b. Just over the top of this is a small 
steel magnet c c, which is attracted the moment an 



electrical current, arriving by the telegraph wire, traverses 
the spirals b b. The magnet c c is rigidly fixed in the 
lever d d, at the other end of which is a style ; this 
makes a mark on a paper band, drawn by a clock-work, as 
often and as long as cc is attracted by the magnetic 
action of the electrical current. Conversely, by reversing 
the magnetism in the iron core of the spirals b b, we 
should obtain in them an electrical current just as we 

PIG. 61. 

have obtained such currents in the magneto-electrical 
machine, Fig. 50 ; in the spirals of that machine there is 
an iron core which, by being approached to the poles of 
the large horse-shoe magnet, is sometimes magnetised in 
one and sometimes in the other direction. 

I will not accumulate examples of such relations; 
in subsequent lectures we shall come across them. Let 
us review these examples once more, and recognise in 
them the law which is common to all. 


A raised weight can produce work, but in doing so it 
must necessarily sink from its height, and, when it has 
fallen as deep as it can fall, its gravity remains as before, 
but it can no longer do work. 

A stretched spring can do work, but in so doing it 
becomes loose. The velocity of a moving mass can do 
work, but in doing so it comes to rest. Heat can perform 
work ; it is destroyed in the operation. Chemical forces 
can perform work, but they exhaust themselves in the 

Electrical currents can perform work, but to keep them 
up we must consume either chemical or mechanical forces, 
or heat. 

We may express this generally. It is a universal 
character of all known natural forces that their capacity 
for work is exhausted in the degree in which they actu- 
ally perform work. 

We have seen, further, that when a weight fell without 
performing any work, it either acquired velocity or pro- 
duced heat. We might also drive a magneto-electrical 
machine by a falling weight ; it would then furnish elec- 
trical currents. 

We have seen that chemical forces, when they come 
into play, produce either heat or electrical currents or 
mechanical work. 

We have seen that heat may be changed into work ; 
there are apparatus (thermo-electric batteries) in which 
electrical currents are produced by it. Heat can directly 
separate chemical compounds ; thus, when we burn lime- 
stone, it separates carbonic acid from lime. 

Thus, whenever the capacity for work of one natural 
force is destroyed, it is transformed into another kind of 
activity. Even within the circuit of inorganic natural 
forces, we can transform each of them into an active 
condition by the aid of any other natural force which is 


capable of work. The connections between the various 
natural forces which modern physics has revealed, are so 
extraordinarily numerous that several entirely different 
methods may be discovered for each of these problems. 

I have stated how we are accustomed to measure 
mechanical work, and how the equivalent in work of heat 
may be found. The equivalent in work of chemical 
processes is again measured by the heat which they pro- 
duce. By similar relations, the equivalent in work of the 
other natural forces may be expressed in terms of mechani- 
cal work. 

If, now, a certain quantity of mechanical work is lost, 
there is obtained, as experiments made with the object of 
determining this point show, an equivalent quantity of 
heat, or, instead of this, of chemical force ; and, conversely, 
when heat is lost, we gain an equivalent quantity of 
chemical or mechanical force ; and, again, when chemical 
force disappears, an equivalent of heat or work ; so that 
in all these interchanges between various inorganic natural 
forces working force may indeed disappear in one form, 
but then it reappears in exactly equivalent quantity in 
some other form ; it is thus neither increased nor dimi- 
nished, but always remains in exactly the same quantity. 
We shall subsequently see that the same law holds good 
also for processes in organic nature, so far as the facts 
have been tested. 

It follows thence that the total quantity of all the forces 
capable of work in the whole universe remains eternal 
and unchanged throughout all their changes. All change 
in nature amounts to this, that force can change its form 
and locality without its quantity being changed. The 
universe possesses, once for all, a store of force which is 
not altered by any change of phenomena, can neither be 
increased nor diminished, and which maintains any change 
which takes place on it. 


You see how, starting from considerations based on the 
immediate practical interests of technical work, we have 
been led up to a universal natural law, which, as far as 
all previous experience extends, rules and embraces all 
natural processes ; which is no longer restricted to the 
practical objects of human utility, but expresses a per- 
fectly general and particularly characteristic property of 
all natural forces, and which, as regards generality, is 
to be placed by the side of the laws of the unalter- 
ability of mass, and the unalterability of the chemical 

At the same time, it also decides a great practical 
question which has been much discussed in the last two 
centuries, to the decision of which an infinity of experi- 
ments have been made and an infinity of apparatus con- 
structedthat is, the question of the possibility of a per- 
petual motion. By this was understood a machine which 
was to work continuously without the aid of any external 
driving force. The solution of this problem promised 
enormous gains. Such a machine would have had all the 
advantages of steam without requiring the expenditure of 
fuel. Work is wealth. A machine which could produce 
work from nothing was as good as one which made gold. 
This problem had thus for a long time occupied the place 
of gold making, and had confused many a pondering 
brain. That a perpetual motion could not be produced 
by the aid of the then known mechanical forces could be 
demonstrated in the last century by the aid of the mathe- 
matical mechanics which had at that time been developed. 
But to show also that it is not possible even if heat, 
chemical forces, electricity, and magnetism were made to 
co-operate, could not be done without a knowledge of 
our law in all its generality. The possibility of a per- 
petual motion was first finally negatived by the law of 
the conservation of force, and this law might also be ex- 


pressed in the practical form that no perpetual motion is 
possible, that force cannot be produced from nothing ; 
something must be consumed. 

You will only be ultimately able to estimate the im- 
portance and the scope of our law when you have before 
your eyes a series of its applications to individual processes 
on nature. 

What I have to-day mentioned as to the origin of the 
moving forces which are at our disposal, directs us to 
something beyond the narrow confines of our laboratories 
and our manufactories, to the great operations at work in 
the life of the earth and of the universe. The force of 
falling water can only flow down from the hills when rain 
and snow bring it to them. To furnish these, we must 
have aqueous vapour in the atmosphere, which can only 
be effected by the aid of heat, and this heat comes from 
the sun. The steam-engine needs the fuel which the 
vegetable life yields, whether it be the still active life of 
the surrounding vegetation, or the extinct life which has 
produced the immense coal deposits in the depths of the 
earth. The forces of man and animals must be restored 
by nourishment ; all nourishment comes ultimately from 
the vegetable kingdom, and leads us back to the same 

You see then that when we inquire into the origin of 
the moving forces which we take into our service, we are 
thrown back upon the meteorological processes in the 
earth's atmosphere, on the life of plants in general, and 
on the sun. 



IN accepting the honour you have done me in request- 
ing me to deliver the first lecture at the opening meeting 
of this year's Association, it appears to me to be more in 
keeping with the import of the moment and the dignity of 
this assembly that, in place of dealing with any particular 
line of research of my own, I should invite you to cast a 
glance at the development of all the branches of physical 
science represented on these occasions. These branches 
include a vast area of special investigation, material 
of almost too varied a character for comprehension, the 
range and intrinsic value of which become greater with 
each year, while no bounds can be assigned to its increase. 
During the first half of the present century we had an 
Alexander von Humboldt, who was able to scan the 
scientific knowledge of his time in its details, and to bring 
it within one vast generalisation. At the present juncture, 
it is obviously very doubtful whether this task could be 
accomplished in a similar way, even by a mind with gifts 
so peculiarly suited for the purpose as Humboldt's was, 
and if all his time and work were devoted to the purpose. 
We. however, working as we do to advance a single 


department of science, can devote but little of our time 
to the simultaneous study of the other branches. As 
soon as we enter upon any investigation, all our powers 
have to be concentrated on a field of narrowed limit. We 
have not only, like the philologian or historian, to seek 
out and search through books and gather from them what 
others have already determined about the subject under 
inquiry ; that is but a secondary portion of our work. 
We have to attack the things themselves, and in doing so 
each offers new and peculiar difficulties of a kind quite 
different from those the scholar encounters ; while in the 
majority of instances, most of our time and labour is con- 
sumed by secondary matters that are but remotely con- 
nected with the purpose of the investigation. 

At one time, we have to study the errors of our instru- 
ments, with a view to their diminution, or, where they 
cannot be removed, to compass tneir detrimental influ- 
ence ; while at other times we have to watch for the 
moment when an organism presents itself under circum- 
stances most favourable for research. Again, in the course 
of our investigation we learn for the first time of possible 
errors which vitiate the result, or perhaps merely raise a 
suspicion that it may be vitiated, and we find ourselves 
compelled to begin the work anew, till every shadow of 
doubt is removed. And it is only when the observer takes 
such a grip of the subject, so fixes all his thoughts and all 
his interest upon it that he cannot separate himself from 
it for weeks, for months, even for years, cannot force 
himself away from it, in short, till he has mastered every 
detail, and feels assured of all those results which must 
come in time, that a perfect and valuable piece of work 
is done. You are all aware that in every good research, 
the preparation, the secondary operations, the control of 
possible errors, and especially in the separation of the 
results attainable in the time from those that cannot 


be attained, consume far more time than is really re- 
quired to make actual observations or experiments. How 
much more ingenuity and thought are expended in 
bringing a refractory piece of brass or glass into sub- 
jection, than in sketching out the plan of the whole 
investigation! Each of you will have experienced such 
impatience and over-excitement during work where all 
the thoughts are directed on a narrow range of ques- 
tions, the import of which to an outsider appears trifling 
and contemptible because he does not see the end to which 
the preparatory work tends. I believe I am correct in 
thus describing the work and mental condition that pre- 
cedes all those great results which hastened so much the 
development of science after its long inaction, and gave 
it so powerful an influence over every phase of human 

The period of work, then, is no time for broad com- 
prehensive survey. When, however, the victory over 
difficulties has happily been gained, and results are secured, 
a period of repose follows, and our interest is next 
directed to examining the bearing of the newly esta- 
blished facts, and once more venturing on a wider survey 
of the adjoining territory. This is essential, and those 
only who are capable of viewing it in this light can 
hope to find useful starting-points for further investi- 

The preliminary work is followed by other work, treat- 
ing of other subjects. In the course of its different 
stages, the observer will not deviate far from a direction 
of more or less narrowed range. For it is not alone of 
importance to him that he may have collected information 
from books regarding the region to be explored. The 
human memory is, on the whole, proportionately patient, 
and can store up an almost incredibly large amount of 
learning. In addition, however, to the knowledge which 


the student of science acquires from lectures and books, 
he requires intelligence which only an ample and diligent 
perception can give him; he needs skill which comes 
only by repeated experiment and long practice. His 
senses must be sharpened for certain kinds of observation, 
to detect minute differences of form, colour, solidity, 
smell, &c., in the object under examination ; his hand 
must be equally trained to the work of the blacksmith, 
the locksmith, and the carpenter, or the draughtsman and 
the violin-player, and, when operating with the micro- 
scope, must surpass the lace-maker in delicacy of handling 
the needle. Moreover, when he encounters superior de- 
structive forces, or performs bloody operations upon man 
or. beast, he must possess the courage and coolness of 
the soldier. Such qualities and capabilities, partly the 
result of natural aptitude, partly cultivated by long 
practice, are not so readily and so easily acquired as the 
mere massing of facts in the memory ; and hence it 
happens that an investigator is compelled, during the 
entire labours of his life, to strictly limit his field, and to 
confine himself to those branches which suit him best. 

We must not, however, forget that the more the in- 
dividual worker is compelled to narrow the sphere of his 
activity, so much the more will his intellectual desire? 
induce him not to sever his connection with the subject 
in its entirety. How shall he go stout and cheerful to 
his toilsome work, how feel confident that what has given 
him so much labour will not moulder uselessly away, but 
remain a thing of lasting value, unless he keeps alive 
within himself the conviction that he also has added a 
fragment to the stupendous whole of Science which is 
to make the reasonless forces of nature subservient to 
the moral purposes of humanity ? 

An immediate practical use cannot generally be counted 
on a priori for each particular investigation. Physical 


science, it is true, has by the practical realisation of its 
results transformed the entire life of modern humanity. 
But, as a rule, these applications appear under circum- 
stances when they are least expected ; to search in that 
direction generally leads to nothing unless certain points 
have already been definitely fixed, so that all that has to 
be done is to remove certain obstacles in the way of prac- 
tical application. If we search the records of the most 
important discoveries, they are either, especially in earlier 
times, made by workmen who their whole lives through 
did but one kind of work, and, either by a happy accident, 
or by a searching, repeated, tentative experiment, hit 
upon some new method advantageous to their particular 
handicraft ; others there are, and this is especially the 
case in most of the recent discoveries, which are the 
fruit of a matured scientific acquaintance with the sub- 
ject in question, an acquaintance that in each instance 
had originally been acquired without any direct view to 
possible use. 

Our Association represents the whole of natural science. 
To-day are assembled mathematicians, physicists, chemists 
and zoologists, botanists and geologists, the teacher of 
science and the physician, the technologist and the ama- 
teur who finds in scientific pursuits relaxation from other 
occupation. Here each of us hopes to meet with fresh 
impulse and encouragement for his peculiar work ; the 
mail who lives in a small country place hopes to meet 
with the recognition, otherwise unattainable, of having 
aided in the advance of science ; he hopes by intercourse 
with men pursuing more or less the same object to mark 
the aim of new researches. We rejoice to find among us 
a goodly proportion of members representing the culti- 
vated classes of the nation ; we see influential statesmen 
among us. They all have an interest in our labours ; 
they look to us for further progress in civilisation, further 


victories over the powers of nature. They it is who 
place at our disposal the actual means for carrying on our 
labours, and are therefore entitled to enquire into the 
results of those labours. It appears to me, therefore, 
appropriate to this occasion to take account of the pro- 
gress of science as a whole, of the objects it aspires to, 
and the magnitude of the efforts made to attain them. 

Such a survey is desirable ; that it lies beyond the 
powers of any one man to accomplish with even an ap- 
proximate completeness such a task as this is clear from 
what I have already said. If I stand here to-day with 
such a problem entrusted to me, my excuse must be that 
no other would attempt it, and I hold that an attempt to 
accomplish it, even if with small success, is better than 
none whatever. Besides, a physiologist has perhaps more 
than all others immediate occasion to maintain a clear 
and constant view of the entire field, for in the present 
state of things it is peculiarly the lot of the physiologist 
to receive help from all other branches of science and to 
stand in alliance with them. In physiology, in fact, the 
importance of the vast strides to which I shall allude, 
has been chiefly felt, while to physiology, and the leading 
controversies arising in it, some of the most valuable 
discoveries are directly due. 

If I leave considerable gaps in my survey, my excuse 
must be the magnitude of the task, and the fact that the 
pressing summons of my friend the secretary of this Asso- 
ciation reached me but recently, and that too in the course 
of my summer holiday in the mountains. The gaps 
which I may leave will at all events be abundantly filled 
up by the proceedings of the Sections. 

Let us then proceed to our task. In discussing the 
progress of physical science as a whole, the first question 
which presents itself is, By what standard are we to 
estimate this progress ? 


To the uninitiated, this science of ours is an accumula- 
tion of a vast number of facts, some of which are con- 
spicuous for their practical utility, while others are 
merely curiosities, or objects of wonder. And, if it were 
possible to classify this unconnected mass of facts, as was 
done in the Linnean system, or in encyclopaedias, so that 
each may be readily found when required, such knowledge 
as this would not deserve the name of science, nor satisfy 
either the scientific wants of the human mind, or the 
desire for progressive mastery over the powers of nature. 
For the former requires an intellectual grasp of the con- 
nection of ideas, the latter demands our anticipation of a 
result in cases yet untried, and under conditions that we 
propose to introduce in the course of our experiment. 
Both are obviously arrived at by a knowledge of the law 
of the phenomena. 

Isolated facts and experiments have in themselves no 
value, however great their number may be. They only be- 
come valuable in a theoretical or practical point of view 
when they make us acquainted with the law of a series 
of uniformly recurring phenomena, or, it may be, only 
give a negative result showing an incompleteness in our 
knowledge of such a law, till then held to be perfect. 
From the exact and universal conformity to law of natural 
phenomena, a single observation of a condition that we 
may presume to be rigorously conformable to law, suffices, 
it is true, at times to establish a rule with the highest 
degree of probability ; just as, for example, we assume our 
knowledge of the skeleton of a prehistoric animal to be 
complete if we find only one complete skeleton of a single 
individual. But we must not lose sight of the fact that 
the isolated observation is not of value in that it is 
isolated, but because it is an aid to the knowledge of the 
conformable regularity in bodily structure of an entire 
species of organisms. In like manner, the knowledge of 


the specific heat of one small fragment of a new metal is 
important because we have no grounds for doubting that 
any other pieces of the same metal subjected to the same 
treatment will yield the same result. 

To find the law by which they are regulated is to 
understand phenomena. For law is nothing more than 
the general conception in which a series of similarly 
recurring natural processes may be embraced. Just as 
we include in the conception ' mammal ' all that is common 
to the man, the ape, the dog, the lion, the hare, the horse, 
the whale, &c., so we comprehend in the law of refraction 
that which we observe to regularly recur when a ray of 
light of any colour passes in any direction through the 
common boundary of any two transparent media. 

A law of nature, however, is not a mere logical con- 
ception that we have adopted as a kind of memoria 
technica to enable us to more readily remember facts. 
We of the present day have already sufficient insight to 
know that the laws of nature are not things which we can 
evolve by any speculative method. On the contrary, we 
have to discover them in the facts ; we have to test them 
by repeated observation or experiment, in constantly new 
cases, under ever-varying circumstances ; and in propor- 
tion only as they hold good under a constantly increasing 
change of conditions, in a constantly increasing number 
of cases and with greater delicacy in the means of ob- 
servation, does our confidence in their trustworthiness 

Thus the laws of nature occupy the position of a power 
with which we are not familiar, not to be arbitrarily 
selected and determined in our minds, as one might 
devise various systems of animals and plants one after 
another, so long as the object is only one of classification. 
Before we can say that our knowledge of any one law 
of nature is complete, we must see that it holds good 


without exception, and make this the test of its correct- 
ness. If we can be assured that the conditions under 
which the law operates have presented themselves, the 
result must ensue without arbitrariness, without choice, 
without our co-operation, and from the very necessity 
which regulates the things of the external world as well 
as our perception. The law then takes the form of an 
objective power, and for that reason we call it force. 

For instance, we regard the law of refraction objectively 
as a refractive force in transparent substances ; ' the law of 
chemical affinity as the elective force exhibited by dif- 
ferent bodies towards one another. In the same way, we 
speak of electrical force of contact of metals, of a force 
of adhesion, capillary force, and so on. Under these 
names are stated objectively laws which for the most part 
comprise small series of natural processes, the conditions 
of which are somewhat involved. In science our con- 
ceptions begin in this way, proceeding to generalizations 
from a number of well-established special laws. We must 
endeavour to eliminate the incidents of form and dis- 
tribution in space which masses under investigation may 
present by trying to find from the phenomena attending 
large visible masses laws for the operation of infinitely 
small particles ; or, expressed objectively, by resolving 
the forces of composite masses into the forces of their 
smallest elementary particles. But precisely in this, 
the simplest form of expression of force namely, of 
mechanical force acting on a point of the mass is it 
especially clear that force is only the law of action ob- 
jectively expressed. The force arising from the presence 
of such and such bodies is equivalent to the acceleration 
of the mass on which it operates multiplied by this mass. 
The actual meaning of such an equation is that it ex- 
presses the following law : if such and such masses are 
present and no other, such and such acceleration of their 


individual points occurs. Its actual signification may be 
compared with the facts and tested by them. The ab- 
stract conception of force we thus introduce implies 
moreover, that we did not discover this law at random, 
that it is an essential law of phenomena. 

Our desire to comprehend natural phenomena, in other 
words, to ascertain their laws, thus takes another form 
of expression that is, we have to seek out the forces 
which are the causes of the phenomena. The conformity 
to law in nature must be conceived as a causal connection 
the moment we recognise that it is independent of our 
thought and will. 

If then we direct our inquiry to the progress of physical 
science as a whole, we shall have to judge of it by the 
measure in which the recognition and knowledge of a 
causative connection embracing all natural phenomena 
has advanced. 

On looking back over the history of our sciences, the 
first great example we find of the subjugation of a wide 
mass of facts to a comprehensive law, occurred in the case 
of theoretical mechanics, the fundamental conception of 
which was first clearly propounded by Galileo. The 
question then was to find the general propositions that to 
us now appear so self-evident, that all substance is inert, 
and that the magnitude of force is to be measured not by 
its velocity, but by changes in it. At first the operation 
of a continually acting force could only be represented as 
a series of small impacts. It was not till Leibnitz and 
Newton, by the discovery of the differential calculus, had 
dispelled the ancient darkness which enveloped the con- 
ception of the infinite, and had clearly established the 
conception of the Continuous and of continuous change, 
that a full and productive application of the newly-found 
mechanical conceptions made any progress. The most 
singular and most splendid instance of such an applica- 


tion was in regard to the motion of the planets, and I 
need scarcely remind you here how brilliant an example 
astronomy has been for the development of the other 
branches of science. In its case, by the theory of gravi- 
tation, a vast and complex mass of facts were first 
embraced in a single principle of great simplicity, and 
such a reconciliation of theory and fact established as 
has never been accomplished in any other department of 
science, either before or since. In supplying the wants of 
astronomy, have originated almost all the exact methods 
of measurement as well as the principal advances made 
in modern mathematics ; the science itself was peculiarly 
fitted to attract the attention of the general public, partly 
by the grandeur of the objects under investigation, partly 
by its practical utility in navigation and geodesy, and 
the many industrial and social interests arising from 

Galileo began with the study of terrestrial gravity. 
Newton extended the application, at first cautiously and 
hesitatingly, to the moon, then boldly to all the planets. 
And, in more recent times, we learn that these laws of the 
common inertia and gravitation of all ponderable masses 
hold good of the movements of the most distant double 
stars of which the light has yet reached us. 

During the latter half of the last and the first half of the 
present century came the great progress of chemistry 
which conclusively solved the ancient problem of dis- 
covering the elementary substances, a task to which so 
much metaphysical speculation had been devoted. Reality 
has always far exceeded even the boldest and wildest 
speculation, and, in the place of the four primitive meta- 
physical elements fire, water, air, and earth we have now 
the sixty-five simple bodies of modern chemistry. Science 
has shown that these elements are really indestructible, un- 
alterable in their mass, unalterable also in their properties ; 


in short, that from every condition into which they may 
have been converted, they can invariably be isolated, and 
recover those qualities which they previously possessed in 
the free state. Through all the varied phases of the 
phenomena of animated and inanimate nature, so far as 
we are acquainted with them, in all the astonishing results 
of chemical decomposition and combination, the number 
and diversity of which the chemist with unwearied dili- 
gence augments from year to year, the one law of the 
immutability of matter prevails as a necessity that knows 
no exception. And chemistry has already pressed on into 
the depths of immeasurable space, and detected in the 
most distant suns or nebulae indications of well-known 
terrestrial elements, so that doubts respecting the pre- 
vailing homogeneity of the matter of the universe no 
longer exist, though certain elements may perhaps be 
restricted to certain groups of the heavenly bodies. 

From this invariability of the elements follows another 
and wider consequence. Chemistry shows by actual experi- 
ment that all matter is made up of the elements which 
have been already isolated. These elements may exhibit 
great differences as regards combination or mixture, the 
mode of aggregation or molecular structure that is to 
say, they may vary the mode of their distribution in 
space. In their properties, on the other hand, they are 
altogether unchangeable ; in other words, when referred 
to the same compound, as regards isolation, and to the 
same state of aggregation, they invariably exhibit the 
same properties as before. If, then, all elementary sub- 
stances are unchangeable in respect to their properties, 
and only changeable as regards their combination and 
their states of aggregation that is, in respect to their 
distribution in space it follows that all changes in the 
world are changes in the local distribution of elementary 
matter, and are eventually brought about through Motion, 


If, however, motion be the primordial change which 
lies at the root of all the other changes occurring in the 
world, every elementary force is a force of motion, and the 
ultimate aim of physical science must bo to determine 
the movements which are the real causes of all other 
phenomena anddiscover the motive powers *vn wTnVh f.h^y^ 
depend: in other words, to merge itself jnfn Tnftp.lia.m'p.g,, 

Though this is clearly the final consequence of the 
qualitative and quantitative immutability of matter, it is 
after all an ideal proposition, the realization of which is 
still very remote. The field is a prescribed one, in which 
we have succeeded in tracing back actually observed 
changes to motions and forces of motion of a definite 
kind. Besides astronomy, may be mentioned the purely 
mechanical part of physics, then acoustics, optics, and 
electricity ; in the science of heat and in chemistry, 
strenuous endeavours are being made towards perfecting 
definite views respecting the nature of the motion and 
position of molecules, while physiology has scarcely made 
a definite step in this direction. 

This renders all the more important, therefore, a note- 
worthy advancement of the most general importance made 
during the last quarter of a century in the direction we are 
considering. If all elementary forces are forces of motion, 
and all, consequently, of similar nature, they should all 
be measurable by the same standard, that is, the standard 
of the mechanical forces. And that this is actually the 
fact is now regarded as proved. The law expressing this 
is known under the name of the law of the Conservation 
of Force. 

For a small group of natural phenomena it had already 
been pronounced by Newton, then more definitely and in 
more general terms by D. Bernouilli, and so continued of 
recognised application in the greater part of the then 
known purely mechanical processes. Certain amplifica- 


tions at times attracted attention, like those of Kumford, 
Davy, and Montgolfier. The first, however, to compass 
the clear and distinct idea of this law, and to venture to 
pronounce its absolute universality, was one whom we 
shall have soon the pleasure of hearing from this platform, 
Dr. Eobert Mayer, of Heilbronn. While Dr. Mayer was 
led by physiological questions to the discovery of the 
most general form of this law, technical questions in 
mechanical engineering led Mr. Joule, of Manchester, 
simultaneously, and independently of him, to the same 
considerations ; and it is to Mr. Joule that we are indebted 
for those important and laborious experimental researches 
in that department where the applicability of the law of 
the conservation of force appeared most doubtful, and 
where the greatest gaps in actual knowledge occurred, 
namely, in the production of work from heat, and of heat 
from work. 

To state the law clearly it was necessary, in con- 
tradistinction to Galileo's conception of the intensity 
of force, that a new mechanical idea was elaborated, 
which we may term the conception of the quantity of 
force, and which has also been called quantity of work 
or of energy. 

A way to this conception of the quantity of force had 
been prepared partly, in theoretical mechanics, through 
the conception of the amount of vis viva of a moving 
body, and partly by practical mechanics through the 
conception of the motive power necessary to keep a 
machine at work. Practical machinists had already 
found a standard by which any motive power could be 
measured, in the determination of the number of pounds 
that it could lift one foot in a second ; and, as is known, 
a horse-power was defined to be equivalent to the motive 
power required to lift seventy kilogrammes one metre ID 
each second. 


Machines, and the motive powers required for their 
movement, furnish, in fact, the most familiar illustra- 
tions of the uniformity of all natural forces expressed by 
the law of the conservation of force. Any machine which 
is to be set in motion requires a mechanical motive 
power. Whence this power is derived or what its form, 
is of no consequence, provided only it be sufficiently 
great and act continuously. At one time we employ a 
steam-engine, at another a water-wheel or turbine, here 
horses or oxen at a whim, there a windmill, or if but 
little power is required, the human arm, a raised weight, 
or an electro-magnetic engine. The choice of the machine 
is merely dependent on the amount of power we would 
use, or the force of circumstance. In the watermill the 
weight of the water flowing down the hills is the agent ; 
it is lifted to the hills by a meteorological process, and 
becomes the source of motive power for the mill. In the 
windmill it is the vis viva of the moving air which 
drives round the sails ; this motion also is due to a 
meteorological operation of the atmosphere. In the steam- 
engine we have the tension of the heated vapour which 
drives the piston to and fro ; this is engendered by the 
heat arising from the combustion of the coal in the fire- 
box, in other words, by a chemical process ; and in this 
case the latter action is the source of the motive power. 
If it be a horse or the human arm which is at work, we 
have the muscles stimulated through the nerves, directly 
producing the mechanical force. In order, however, that 
the living body may generate muscular power it must be 
nourished and breathe. The food it takes separates again 
from it, after having combined with the oxygen inhaled 
from the air, to form carbonic acid and water. Here 
again, then, a chemical process is an essential element to 
maintain muscular power. A similar state of things is ob- 
served in the electro-magnetic machines of our telegraphs. 


Thus, then, we obtain mechanical motive force from 
the most varied processes of nature in the most different 
ways; but it will also be remarked in only a limited 
quantity. In doing so we always consume something that 
nature supplies to us. In the watermill we use a quantity 
of water collected at an elevation, coal in the steam- 
engine, zinc and sulphuric acid in the electro-magnetic 
machine, food for the horse ; in the windmill we use up 
the motion of the wind, which is arrested by the sails. 

Conversely, if we have a motive force at our disposal 
we can develop with it forms of action of the most varied 
kind. It will not be necessary in this place to enumerate 
the countless diversity of industrial machines, and the 
varieties of work which they perform. 

Let us rather consider the physical differences of the 
possible performance of a motive power. With its help 
we can raise loads, pump water to an elevation, compress 
gases, set a railway train in motion, and through friction 
generate heat. By its aid we can turn magneto-electric 
machines, and produce electric currents, and with them 
decompose water and other chemical compounds having 
the most powerful affinities, render wires incandescent, 
magnetise iron> &c. 

Moreover, had we at our disposal a sufficient me- 
chanical motive force we could lestore all those states 
and conditions from which, as was seen above, we are 
enabled at the outset to derive mechanical motive power. 

As, however, the motive power derived from any 
given natural process is limited, so likewise is there a 
limitation to the total amount of modifications which we 
may produce by the use of any given motive power. 

These deductions, arrived at first in isolated instances 
from machines and physical apparatus, have now been 
welded into a law of nature of the widest validity. Every 
thange in nature is equivalent to a certain development, 


or a certain consumption of motive force. If motive 
power be developed it may either appear as such, or be 
directly used up again to form other changes equivalent 
in magnitude. The leading determinations of this equiva- 
lency are founded on Joule's measurements of the me- 
chanical equivalent of heat. When, by the application 
of heat, we set a steam-engine in motion, heat propor- 
tional to the work done disappears within it; in short, 
the heat which can warm a given weight of water one 
degree of the Centigrade scale is able, if converted into 
work, to lift the same weight of water to a height of 
425 metres. If we convert work into heat by friction 
we again use, in heating a given weight of water one 
degree Centigrade, the motive force which the same 
quantity of water would have generated in flowing down 
from a height of 425 metres. Chemical processes gene- 
rate heat in definite proportion, and in like manner we 
estimate the motive power equivalent to such chemical 
forces; and thus the energy of the chemical force of 
affinity is also measurable by the mechanical standard. 
The same holds true for all the other forms of natural 
forces, but it will not be necessary to pursue the subject 
further here. 

It has actually been established, then, as a result of 
these investigations, that all the forces of nature are 
measurable by the same mechanical standard, and that 
all pure motive forces are, as regards performance of 
work, equivalent. And thus one great step towards the 
solution of the comprehensive theoretical task of referring 
all natural phenomena to motion has been accomplished. 

Whilst the foregoing considerations chiefly seek to 
elucidate the logical value of the law of the conservation 
of force, its actual signification in the general conception 
of the processes of nature is expressed in the grand con- 
nection which it establishes between the entire processes 


of the universe, through all distances of place or time. 
The universe appears, according to this law, to be en- 
dowed with a store of energy which, through all the 
varied changes in natural processes, can neither be 
increased nor diminished, which is maintained therein 
in ever-varying phases, but, like matter itself, is from 
eternity to eternity of unchanging magnitude ; acting 
in space* but not divisible, as matter is, with it. Every 
change in the world simply consists in a variation in the 
mode of appearance of this store of energy. Here we 
find one portion of it as the vis viva of moving bodies, 
there as regular oscillation in light and sound ; or, again, 
as heat, that is to say, the irregular motion of invisible 
particles ; at another point the energy appears in the 
form of. the weight of two masses gravitating towards 
each other, then as internal tension and pressure of 
elastic bodies, or as chemical attraction, electrical ten- 
sion, or magnetic distribution. If it disappear in one 
form, it reappears as surely in another ; and whenever 
it presents itself in a new phase we are certain that 
it does so at the expense of one of its other forms. 

Carnot's law of the mechanical theory of heat, as 
modified by Clausius, has, in fact, made it clear that 
this change moves in the main continuously onward in a 
definite direction, so that a constantly increasing amount 
of the great store of energy in the universe is being 
transformed into heat. 

We can, therefore, see with the mind's eye the original 
condition of things in which the matter composing the 
celestial bodies was still cold, and probably distributed 
as chaotic vapour or dust through space ; we see that 
it must have developed heat when it collected together 
under the influence of gravity. Even at the present 
time spectrum analysis (a method the theoretical prin- 
ciples of which owe their origin to the mechanical theory 


of beat) enables us to detect remains of this loosely 
distributed matter in the nebulae ; we recognise it in the 
meteor-showers and comets ; the act of agglomeration 
and the development of heat still continue, though in 
our portion of the stellar system they have ceased to 
a great extent. The chief part of the primordial 
energy of the matter belonging to our system is now 
in the form of solar heat. This energy, however, will 
not remain locked up in our system for ever : portions 
of it are continually radiating from it, in the form of 
light and heat, into infinite space. Of this radiation 
our earth receives a share. It is these solar heat-rays 
which produce on the earth's surface the winds and the 
currents of the ocean, and lift the watery vapour from 
the tropical seas, which, distilling over hill and plain, 
returns as springs and rivers to the sea. The solar rays 
impart to the plant the power to separate from carbonic 
acid and water those combustible substances which serve 
as food for animals, and thus, in even the varied changes 
of organic life, the moving power is derived from the 
infinitely vast store of the universe. 

This exalted picture of the connection existing between 
all the processes of nature has been often presented to 
us in recent times ; it will suffice here that I direct 
attention to its leading features. If the task of physical 
science be to determine laws, a step of the most com- 
prehensive significance towards that object has here been 

The application of the law of the conservation of force 
to the vital processes of animals and plants, which has 
just been discussed, leads us in another direction in 
which our knowledge of nature's conformity to law has 
made an advance. The law to which we referred is 
of the most essential importance in leading questions 
of physiology, and it was for this reason that Dr. Mayer 


and I were led on physiological grounds to investigations 
having especial reference to the conservation of force. 

As regards the phenomena of inorganic nature all 
doubts have long since been laid to rest respecting the 
principles of the method. It was apparent that these 
phenomena had fixed laws, and examples enough were 
already known to make the finding of such laws probable. 

In consequence, however, of the greater complexity of 
the vital processes, their connection with mental action, 
and the unmistakable evidence of adaptability to a pur- 
pose which organic structures exhibit, the existence of a 
settled conformity to law might well appear doubtful, and, 
in fact, physiology has always had to encounter this 
fundamental question : are all vital processes absolutely 
conformable to law ? Or is there, perhaps, a range of 
greater or less magnitude within which an exception 
prevails r More or less obscured by words, the view of 
Paracelsus, Helmont, and Stahl, has been, and is at 
present, held, particularly outside Germany, that there 
exists a soul of life (" Lebensseele ") directing the organic 
processes which is endowed more or less with conscious- 
ness like the soul of man. The influence of the inorganic 
forces of nature on the organism was still recognised 
on the assumption that the soul of life only exercises 
power over matter by means of the physical and chemical 
forces of matter itself; so that without this aid it could 
accomplish nothing, but that it possessed the faculty of 
suspending or permitting the operation of the forces 
at pleasure. 

After death, when no longer subject to the control of 
the soul of life or vital force, it was these very chemical 
forces of organic matter which brought about decomposi- 
tion. In short, through all the different modes of ex- 
pressing it, whether it was termed the Archaus, the 
anima inscia, or the vital force and the restorative 


poiver of nature, the faculty to build up the body accord- 
ing to system, and to suitably accommodate it to external 
circumstances, remained the most essential attribute of 
this hypothetically controlling principle of the vitalistic 
theory with which, therefore, by reason of its attributes, 
only the name of soul fully harmonised. 

It is apparent, however, that this notion runs directly 
counter to the law of the conserva^n of force. If vital 
force were for a time to annul the gravity of a weight, 
it could be raised without labour to any desired height, 
and subsequently, if the action of gravity were again 
restored, could perform work of any desired magnitude. 
And thus work could be obtained out of nothing without 
expense. If vital force could for a time suspend the 
chemical affinity of carbon for oxygen, carbonic acid 
could be decomposed without work being employed for 
that purpose, and the liberated carbon and oxygen 
could perform new work. 

In reality, however, no trace of such an action is to 
be met with as that of the living organism being able 
to generate an amount of work without an equivalent 
expenditure. When we consider the work done by 
animals, we find the operation comparable in every 
respect with that of the steam-engine. Animals, like 
machines, can only move and accomplish work by being 
continuously supplied with fuel (that is to say, food) and 
air containing oxygen ; both give off again this material 
in a burnt state, and at the same time produce heat and 
work. All investigation, thus far, respecting the amount 
of heat which an animal produces when at rest is in 
no way at variance with the assumption that this heat 
exactly corresponds to the equivalent, expressed as work, 
of the forces of chemical affinity then in action. 

As regards the work done by plants, a source of power 
in every way sufficient, exists in the solar rays which they 


require for the increase of the organic matter of their 
structures. Meanwhile it is true that exact quantitative 
determinations of the equivalents of force, consumed and 
produced in the vegetable as well as the animal kingdom, 
have still to be made in order to fully establish the 
exact accordance of these two values. 

If, then, the law of the conservation of force hold 
good also for the living body, it follows that the physical 
and chemical forces of the material employed in building- 
up the body are in continuous action without inter- 
mission and without choice, and that their exact con- 
formity to law never suffers a moment's interruption. 

Physiologists, then, must expect to meet with an un- 

! conditional conformity to law of the forces of nature 
in their inquiries respecting the vital processes; they 
will have to apply themselves to the investigation of the 
physical and chemical processes going on within the 
organism. It is a task of vast complexity and extent ; 
but the workers, in Germany especially, are both nu- 
merous and enthusiastic, and we may already affirm 
that their labours have not been unrewarded, inasmuch 
as our knowledge of the vital phenomena has made 
greater progress during the last forty years than in the 
two preceding centuries. 

Assistance, that cannot be too highly valued, towards 
the elucidation of the fundamental principles of the 
doctrine of life, has been rendered on the part of descrip- 
tive natural history, through Darwin's theory of the 
evolution of organic forms, by which the possibility of 
an entirely new interpretation of organic adaptability is 

The adaptability in the construction of the functions 
of the living body, most wonderful at any time, and 
with the progress of science becoming still more so, was 
doubtless the chief reason that provoked a comparison 


of the vital processes with the actions of a principle 
acting like a soul. In the whole external world we know 
of but one series of phenomena possessing similar 
characteristics, we mean the actions and deeds of an 
intelligent human being ; and we must allow that in 
innumerable instances the organic adaptability appears to 
be so extraordinarily superior to the" capacities of the 
human intelligence that we might feel disposed to ascribe 
to it a higher rather than a lower character. 

Before the time of Darwin cnly two theories respect- 
ing organic adaptability were in vogue, both of which 
pointed to the interference of free intelligence in the 
course of natural processes. On the one hand it was 
held, in accordance with the vitalistic theory, that the 
vital processes were continuously directed by a living 
soul ; or, on the other, recourse was had to an act of 
supernatural intelligence to account for the origin of 
every living species. The latter view indeed supposes 
that the causal connection of natural phenomena had been 
broken less often, and allows of a strict scientific examina- 
tion of the processes observable in the species of human 
beings now existing ; but even it is not able to entirely 
explain away those exceptions to the law of causality, 
and consequently it enjoyed no considerable favour as 
opposed to the vitalistic view, which was powerfully 
supported, by apparent evidence, that is, by the natural 
desire to find similar causes behind similar phenomena. 

Darwin's theory contains an essentially new creative 
thought. It shows how adaptability of structure in 
organisms can result from a blind rule of a law 
of nature without any intervention of intelligence. I 
allude to the law of transmission of individual pecu- 
liarities from parent to offspring, a law long known 
and recognised, and only needing a more precise defi- 
nition. If both parents have individual peculiarities 


in common, the majority of their offspring also possess 
them ; and if among the offspring there are some which 
present these peculiarities in a less marked degree, there 
will, on the other hand, always be found among a great 
number, others in which the same peculiarities have 
become intensified. If, now, these be selected to propa- 
gate offspring, a greater and greater intensification of 
these peculiarities may be attained and transmitted. 
This is, in fact, the method employed in cattle-breeding 
and gardening, in order with greater certainty to obtain 
new breeds and varieties, with well-marked different 
characters. The experience of artificial breeding is to 
be regarded, from a scientific point of view, as an ex- 
perimental confirmation of the law under discussion ; 
and, in fact, this experiment has proved successful, and 
is still doing so, with species of every class of the animal 
kingdom, and, with respect to the most different organs 
of the body, in a vast number of instances. 

After the general application of the law of trans- 
mission had been established in this way, it only re- 
mained for Darwin to discuss the bearings of the question 
as regards animals and plants in the wild state. The 
result which has been arrived at is that those individuals 
whicli are distinguished in the struggle for existence 
by some advantageous quality, are the most likely to 
produce offspring, and thus transmit to them their ad- 
vantageous qualities. And in this way from generation 
to generation a gradual adjustment is arrived at in the 
adaptation of each species of living creation to the 
conditions under which it has to live until the type 
has reached such a degree of perfection that any sub- 
stantial variation from it is a disadvantage. It will 
then remain unchanged so long as the external con- 
ditions of its existence remain materially unaltered. 
Such an almost absolutely fixed condition appears to 


be attained by the plants and animals now living, and 
thus the continuity of the species, at least during 
historic times, is found to prevail. 

An animated controversy, however, still continues, con- 
cerning the truth or probability of the Darwinian theory, 
for the most part respecting the limits that should be 
assigned to the variation of species. The opponents of 
this view would hardly deny that, as assumed by Darwin, 
hereditary differences of race could have arisen in one 
and the same species ; or, in other words, that many of 
the forms hitherto regarded as distinct species of the same 
genus have been derived from the same primitive form. 
Whether we must restrict our view to this, or whether, 
perhaps, we venture to derive all mammals from one origi- 
nal marsupial, or, again, all vertebrates from a primitive 
lancelet, or all plants and animals together from the slimy 
protoplasm of a protiston, depends at the present moment 
rather on the leanings of individual observers than on 
facts. Fresh links, connecting classes of apparently 
irreconcilable type, are always presenting themselves ; 
the actual transition of forms, into others widely different, 
has already been traced in regularly deposited geological 
strata, and has come to be beyond question ; and since 
this line of research has been taken up, how numerous 
are the facts which fully accord with Darwin's theory, 
and give special effect to it in detail ! 

At the same time, we should not forget the clear in- 
terpretation Darwin's grand conception has supplied of 
the till then mysterious notions respecting natural affinity, 
natural systems, and homology of organs in various 
animals ; how by its aid the remarkable recurrence of 
the structural peculiarities of lower animals in the 
embryos of others higher in the scale, the special kind 
of development appearing in the series of palseontological 
forms, and the peculiar conditions of affinity of the faunas 


and floras of limited areas have, one and all, received 
elucidation. Formerly natural affinity appeared to be a 
mere enigmatical, and altogether groundless similarity 
of forms ; now it has become a matter for actual consan- 
guinity. The natural system certainly forced itself as 
such upon the mind, although theory strictly disavowed 
any real significance to it; at present it denotes an 
actual genealogy of organisms. The facts of palseonto- 
logical and embryological evolution and of geographical 
distribution were enigmatical wonders so long as each 
species was regarded as the result of an independent act 
of creation, and cast a scarcely favourable light on the 
strange tentative method which was ascribed to the 
Creator. Darwin has raised all these isolated questions 
from the condition of a heap of enigmatical wonders 
to a great consistent system of development, and esta- 
blished definite ideas in the place of such a fanciful 
hypothesis as, among the first, had occurred to Groethe, 
respecting the facts of the comparative anatomy and the 
morphology of plants. 

This renders possible a definite statement of problems 
for further inquiry, a great gain in any case, even should 
it happen that Darwin's theory does not embrace the whole 
truth, and that, in addition to the influences which he has 
indicated, there should be found to be others which 
operate in the modification of organic forms. 

While the Darwinian theory treats exclusively of the 
gradual modification of species after a succession of 
generations, we know that a single individual may adapt 
itself, or become accustomed, in a certain degree, to the 
circumstances under which it has to live ; and that even 
during the single life of an individual a distinct progress 
towards a higher development of organic adaptability 
may be attained. And it is more especially in those 
forms of organic life where the adaptability in structure 


has reached the highest grade and excited the greatest 
admiration, namely, in the region of mental perception, 
that, as the latest results of physiology teach us, this 
individual adaptation plays a most prominent part. 

Who has not marvelled at the fidelity and accuracy 
of the information which our senses convey to us from 
the surrounding world, more especially those of the far- 
reaching eye ? The information so gained furnishes the 
premisses for the conclusions which we come to, the acts 
that we perform ; and unless our senses convey to us 
correct impressions, we cannot expect to act accurately, 
so that results shall correspond with our expectations. 
By the success or failure of our acts we again and again 
test the truth of the information with which our senses 
supply us, and experience, after millions of repetitions, 
shows us that this fidelity is exceedingly great, in fact, 
almost free from exceptions. At all events, these exceptions, 
the so-called illusions of the senses, are rare, and are only 
brought about by very special and unusual circumstances. 

Whenever we stretch forth the hand to lay hold of 
something, or advance the foot to step upon some object, 
we must first form an accurate optical image of the position 
of the object to be touched, its form, distance, &c., or we 
shall fail. The certainty and accuracy of our perception 
by the senses must at least equal the certainty and 
accuracy which our actions have attained after long 
practice ; and the belief, therefore, in the trustworthiness 
of our senses is no blind belief, but one, the accuracy of 
which has been tested and- verified again and again by 
numberless experiments. 

Were this harmony between the perceptions through 
the senses and the objects causing them, in other words, 
this basis of all our knowledge, a direct product of the 
vital principle, its formative power would, in fact, then 
have attained the highest degree of perfection. But an 


examination of the actual facts at once destroys in the 
most merciless manner all belief in a preordained harmony 
of the inner and external world. 

I need not call to mind the startling and unexpected re- 
sults of ophthalmometrical and optical research which have 
proved the eye to be a by no means more perfect optical 
instrument than those constructed by human hands ; but, 
on the contrary, to exhibit, in addition to the faults 
inseparable from any dioptric instrument, others that in 
an artificial instrument we should severely condemn ; nor 
need I remind you that the ear conveys to us sounds from 
without in no wise in the ratio of their actual intensity, 
but strangely resolves them and modifies them, intensify- 
ing or weakening them in very different degrees, ac- 
cording to their varieties of pitch. 

These anomalies, however, are as nothing compared 
with those to be met with in examining the nature of the 
sensations by which we become acquainted with the 
various properties of the objects surrounding us. Here 
it can at once be proved that no kind and no degree of 
similarity exists between the quality of a sensation and 
the quality of the agent inducing it, and portrayed by it. 

In its leading features this was demonstrated by Johannes 
Miiller in his law of the Specific Action of the Senses. Ac- 
cording to him, each nerve of sense possesses a peculiar kind 
of sensation. A nerve, we know, can be rendered active 
by a vast number of exciting agents, and the same agent 
may likewise affect different organs of sense ; but however 
it be brought about, we never have in nerves of sight 
any other sensation than that of light ; in the nerves of 
the ear any other than a sensation of sound; in short, 
in each individual nerve of sense only that sensation 
which corresponds to its peculiar specific action. The 
most marked differences in the qualities of sensation, 
in other words, those between the sensations of different 


senses, are, then, in no way dependent on the nature of 
the exciting agent, but only on that of the nerve appa- 
ratus under operation. 

The bearing of Miiller's law has been extended by 
later research. It appears highly probable that even the 
sensations of different colours and different pitch, as well 
as qualitative peculiarities of luminous sensations inter se, 
and of sonorous sensations inter se, also depend on the 
excitation of systems of fibres, with distinct character 
and endowed with different specific energy, of nerves 
of sight and hearing respectively. The infinitely more 
varied diversity of composite light is in this way refer- 
able to sensations of only threefold heterogeneous 
character, in other words, to mixtures of the three 
primary colours. From this reduction in the number of 
possible differences it follows that very different compo- 
site light may appear the same. In this case it has been 
shown that no kind of physical similarity whatever corre- 
sponds to the subjective similarity of different composite 
light of the same colour. By these and similar facts we are 
led to the very important conclusion that our sensations 
are, as regards their quality, only signs of external 
objects, and in no sense images of any degree of re- 
semblance. An image must, in certain respects, be 
analogous to the original object ; a statue, for instance, 
has the same corporeal form as the human being after 
which it. is made ; a picture the same colour and per- 
spective projection. For a sign it is sufficient that it 
become apparent as often as the occurrence to be de- 
picted makes its appearance, the conformity between 
them being restricted to their presenting themselves 
simultaneously ; and the correspondence existing between 
our sensations and the objects producing them is pre- 
cisely of this kind. They are signs which we have 
learned to decipher, and a language given us with our 


organisation by which external objects discourse to us 
a language, however, like our mother tongue, that we 
can only learn by practice and experience. 

Moreover, what has been said holds good not only for 
the qualitative differences of sensations, but also, in any 
case, for the greatest and most important part, if not the 
whole, of our various perceptions of extension in space. 
In their bearings on this question the new doctrine of 
binocular vision and the invention of the stereoscope 
have been of importance. All that the sensation of the 
two eyes could convey to us directly, and without 
psychical aid was, at the most, two somewhat different 
flat pictures of two dimensions as they lay on the two 
retinae ; instead of this we perceive a representation 
with three dimensions of the things around us. We 
are sensible as well of the distance of objects not 
too far removed from us as of their perspective juxta- 
position^ and compare the actual magnitude of two 
objects of apparently unequal size at different distances 
from us with greater certainty than the apparent equal 
magnitudes of a finger, say, and the moon. 

One explanation only of our perception of extension 
in space, which stands the test of each separate fact, can 
in my judgment be brought forward by our assuming 
with Lotze that to the sensations of nerve- fibres, dif- 
ferently situated in space, certain differences, local signs, 
attach themselves, the significations of which, as regards 
space, we have to learn. That a knowledge of their 
signification may be attained by these hypotheses, and 
\\ith the help of the movements of our body, and that 
we can at the same time learn which are the right move- 
ments to bring about a desired result, and become 
conscious of having arrived at it, has in many ways been 

That experience exercised an enormous influence over 


the signification of visual pictures, and, in cases of doubt, 
is generally the final arbiter, is allowed even by those 
physiologists who wish to save as much as possible of the 
innate harmony of the senses with the external world. 
The controversy is at present almost entirely confined to 
the question of the proportion at birth of the innate 
impulses that can facilitate training in the understanding 
of sensations. The assumption of the existence of im- 
pulses of this kind is unnecessary, and renders difficult 
instead of elucidating an interpretation of well-observed 
phenomena in adults. 1 

It follows, then, that this subtile and most admirable 
harmony existing between our sensations and the objects 
causing them is substantially, and with but few doubtful 
exceptions, a conformity individually acquired, a result 
of experience, of training, the recollection of former acts 
of a similar kind. 

This completes the circle of our observations, and lands 
us at the spot whence we set out. We found at the 
beginning, that what physical science strives after is 
the knowledge of laws, in other words, the knowledge how 
at different times under the same conditions the same 
results are brought about ; and we found in the last 
instance how all laws can be reduced to laws of motion. 
We now find, in conclusion, that our sensations are merely 
signs of changes taking place in the external world, and 
can only be regarded as pictures in that they represent 
succession in time. For this very reason they are in a 
position to show directly the conformity to law, in regard 
to succession in time, of natural phenomena. If, under 
the same natural circumstances, the same action take 
place, a person observing it under the same conditions 
will find the same series of impressions regularly recur. 

1 A further exposition of these conditions will be found in the lectures on 
the Recent Progress of the Theory of Vision, pp. 197 et seq. 


That which our organs of sense perform is clearly suffi- 
cient to meet the demands of science as well as the practical 
ends of the man of business who must rely for support on 
the knowledge of natural laws, acquired, partly involun- 
tarily by daily experience, and partly purposely by the 
study of science. 

Having now completed our survey, we may, perhaps, 
strike a not unsatisfactory balance. Physical science has 
made active progress, not only in this or that direction, 
but as a vast whole, and what has been accomplished 
may warrant the attainment of further progress. Doubts 
respecting the entire conformity to law of nature are 
more and more dispelled ; laws more general and more 
comprehensive have revealed themselves. That the di- 
rection which scientific study has taken is a healthy one 
its great practical issues have clearly demonstrated ; and 
I may here be permitted to direct particular attention 
to the branch of science more especially my own. In 
physiology particularly scientific work had been crippled 
by doubts respecting the necessary conformity to law, 
which means, as we have shown, the intelligibility of 
vital phenomena, and this naturally extended itself to 
the practical science directly dependent on physiology, 
namely, medicine. Both have received an impetus, such 
as had not been felt for thousands of years, from the time 
that they seriously adopted the method of physical science, 
the exact observation of phenomena and experiment. As 
a practising physician, in my earlier days, I can per- 
sonally bear testimony to this. I was educated at a 
period when medicine was in a transitional stage, when 
the minds of the most thoughtful and exact were filled 
with despair. It was not difficult to recognise that the 
old predominant theorising methods of practising medicine 
were altogether untenable ; with these theories, however, 
the facts on which they had actually been founded had 


become so inextricably entangled that they also were 
mostly thrown overboard. How a science should be built 
up anew had already been seen in the case of the other 
sciences ; but the new task assumed colossal proportions ; 
few steps had been taken towards accomplishing it, 
and these first efforts were in some measure but crude 
and clumsy. We need feel no astonishment that many 
sincere and earnest men should at that time have 
abandoned medicine as unsatisfactory, or on principle 
given themselves over to an exaggerated empiricism. 

But well directed efforts produced the right result 
more quickly even than many had hoped for. The 
application of the mechanical ideas to the doctrine of 
circulation and respiration, the better interpretation of 
thermal phenomena, the more refined physiological study 
of the nerves, soon led to practical results of the greatest 
importance ; microscopic examination of parasitic struc- 
tures, the stupendous development of pathological anatomy, 
irresistibly led from nebulous theories to reality. We 
found that we now possessed a much clearer means of 
distinguishing, and a clearer insight into the mechanism 
of the process of disease than the beats of the pulse, the 
urinary deposit, or the fever type of older medical science 
had ever given us. If I might name one department 
of medicine in which the influence of the scientific 
method has been, perhaps, most brilliantly displayed, it 
would be in ophthalmic medicine. The peculiar con- 
stitution of the eye enables us to apply physical modes of 
investigation as well in functional as in anatomical 
derangements of the living organ. Simple physical ex- 
pedients, spectacles, sometimes spherical, sometimes cylin- 
drical or prismatic, suffice, in many cases, to cure dis- 
orders which in earlier times left the organ in a condition 
of chronic incapacity; a great number of changes on 
the other hand, which formerly did not attract notice 


till they induced incurable blindness, can now be 
detected and remedied at the outset. From the very 
reason of its presenting the most favourable ground for 
the application of the scientific method, ophthalmology 
has proved attractive to a peculiarly large number of 
excellent investigators, and rapidly attained its present 
position, in which it sets an example to the other depart- 
ments of medicine, of the actual capabilities of the 
true method, as brilliant as that which astronomy for 
long had offered to the other branches of physical science. 

Though in the investigation of inorganic nature the 
several European nations showed a nearly uniform ad- 
vancement, the recent progress of physiology and medi- 
cine is pre-eminently due to Grermany. I have already 
spoken of the obstacles which formerly delayed progress in 
this direction. Questions respecting the nature of life are 
closely bound up with psychological and ethical inquiries. 
It demands, moreover, that we bestow on it unwearied 
diligence for purely ideal purposes, without any approach- 
ing prospect of the pure science becoming of practical 
value. And we may make it our boast that this exalted 
and self-denying assiduity, this labour for inward satis- 
faction, not for external success, has at all times peculiarly 
distinguished the scientific men of Germany. 

What has, after all, determined the state of things 
in the present instance is in my opinion another cir- 
cumstance, namely, that we are more fearless than others 
of the consequences of the entire and perfect truth. 
Both in England and France we find excellent inves- 
tigators who are capable of working with thorough 
energy in the proper sense of the scientific methods; 
hitherto, however, they have almost always had to bend 
to social or ecclesiastical prejudices, and could only openly 
express their convictions at the expense of their social 
influence and their usefulness. 


Germany has advanced with bolder step : she has had 
the full confidence, which has never been shaken, that 
truth fully known brings with it its own remedy for 
the danger and disadvantage that may here and there 
attend a limited recognition of what is true. A labour- 
loving, frugal, and moral people may exercise such bold- 
ness, may stand face to face with truth ; it has nothing 
to fear though hasty or partial theories be advocated, 
even if they should appear to trench upon the founda- 
tions of morality and society. 

We have met here on the southern frontier of our 
country. In science, however, we recognise no political 
boundaries, for our country reaches as far as the German 
tongue is heard, wherever German industry and German 
intrepidity in striving after truth find favour. And 
that it finds favour here is shown by our hospitable 
reception, and the inspiriting words with which we have 
been greeted. A new medical faculty has been established 
here. We will wish it in its career rapid progress in the 
cardinal virtues of German science, for then it will not 
only find remedies for bodily suffering, but become an- 
active centre to strengthen intellectual independence, 
steadfastness to conviction and love of truth, and at the 
same time be the means of deepening the sense of unity 
throughout our country. 


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